Get the variables using the columns with 1 and 0s. All other variables are zero. The maximum value you are looking for appears in the bottom right hand corner. Exercise 3.4.1 3.4. 1. 1. Use simplex method to solve: Maximize: P = 5x + 7y + 9z P = 5 x + 7 y + 9 z. Subject to:Finding the optimal solution to the linear programming problem by the simplex method. Complete, detailed, step-by-step description of solutions. Hungarian method, dual simplex, matrix games, potential method, traveling salesman problem, dynamic programmingFinding the optimal solution to the linear programming problem by the simplex method. Complete, detailed, step-by-step description of solutions. Hungarian method, dual simplex, matrix games, potential method, traveling salesman problem, dynamic programming Simplex Algorithm Calculator is an online application on the simplex algorithm and two phase method. Inputs Simply enter your linear programming problem as follows 1) Select if the problem is maximization or minimization 2) Enter the cost vector in the space provided, ie in boxes labeled with the Ci. Simplex Algorithm Calculator is an online application on the simplex algorithm and two phase method. Inputs Simply enter your linear programming problem as follows 1) Select if the problem is maximization or minimization 2) Enter the cost vector in the space provided, ie in boxes labeled with the Ci. Finding the optimal solution to the linear programming problem by the simplex method. Complete, detailed, step-by-step description of solutions. Hungarian method, dual simplex, matrix games, potential method, traveling salesman problem, dynamic programmingSimplex Tableau The simplex tableau is a convenient means for performing the calculations required by the simplex method. Setting Up Initial Simplex Tableau Step 1: If the problem is a minimization problem, multiply the objective function by -1. Step 2: If the problem formulation contains any constraints with negative right-hand sides,Mar 13, 2015 · This paper proposes a streamlined form of simplex method which provides some great benefits over traditional simplex method. For instance, it does not need any kind of artificial variables or artificial constraints; it could start with any feasible or infeasible basis of an LP. This method follows the same pivoting sequence as of simplex phase 1 without showing any explicit description of ... The current solution will be infeasible with respect to these constraints. Use the dual simplex method to solve to optimality. If the new optimal solution has all integer values for the x j then again you are done. If not, then click "Add Cuts" again and repeat. Keep repeating until the optimal solution has all integer values for the x j variables. 1.2 The Simplex Method The Simplex Method describes a method for entering inequalities as equations into a matrix and the keys to row-reduce that matrix. This method also is applicable to any number of independent variables, making graphing unnecessary. The following is a demonstration of an activity, including calculator commands, which make ... You can use the parameter method to define the linear programming method that you want to use. There are three options: method="interior-point" selects the interior-point method. This option is set by default. method="revised simplex" selects the revised two-phase simplex method. method="simplex" selects the legacy two-phase simplex method. To multiply two matrices together the inner dimensions of the matrices shoud match. For example, given two matrices A and B, where A is a m x p matrix and B is a p x n matrix, you can multiply them together to get a new m x n matrix C, where each element of C is the dot product of a row in A and a column in B.Game theory. Matrix game solution by linear programming method. Complete, detailed, step-by-step description of solutions. Hungarian method, dual simplex, matrix games, potential method, traveling salesman problem, dynamic programming modi method (optimal solution) calculator - Finding solution of Transportion problem using modi method (optimal solution), step-by-step online We use cookies to improve your experience on our site and to show you relevant advertising. Get the variables using the columns with 1 and 0s. All other variables are zero. The maximum value you are looking for appears in the bottom right hand corner. Exercise 3.4.1 3.4. 1. 1. Use simplex method to solve: Maximize: P = 5x + 7y + 9z P = 5 x + 7 y + 9 z. Subject to:La calculadora Metodo Simplex online que aquí te presentamos permite resolver cualquier tipo de problemas de programacion lineal mediante el uso del método simplex. Para usarla solo debes seguir los siguientes pasos: Si alguna de las variables están restringidas a tomar solo números enteros, deberás indicarlo como una restricción ...Solution Help. Dual simplex method calculator. 1. Find solution using dual simplex method. Minimize Z = 2x1 + 3x2 + 0x3. subject to the constraints. 2x1 - x2 - x3 ≥ 3.La calculadora Metodo Simplex online que aquí te presentamos permite resolver cualquier tipo de problemas de programacion lineal mediante el uso del método simplex. Para usarla solo debes seguir los siguientes pasos: Si alguna de las variables están restringidas a tomar solo números enteros, deberás indicarlo como una restricción ... The solution is to apply the method of the two phases, which consists of the following: Phase 1. 1) We add a dummy variable for each of our restrictions, which will have no impact on them. 3x 1 + 2x 2 + x 3 + x 4 + x 7 = 10. 2x 1 + 5x 2 + 3x 3 + x 5 + x 8 = 15. x 1 + 9x 2 - x 3 - x 6 + x 9 = 4.Simplex Method Calculator - application which is help to find the optimal solution to the linear programming problem by the simplex method. Updated on. Jun 9, 2021.Simplex Tableau The simplex tableau is a convenient means for performing the calculations required by the simplex method. Setting Up Initial Simplex Tableau Step 1: If the problem is a minimization problem, multiply the objective function by -1. Step 2: If the problem formulation contains any constraints with negative right-hand sides, May 10, 2020 · The simplex method is an algorithm for solving linear programming problems. It is based on the fact that an optimal solution to a linear programming problem always lies at an extreme point. This fact leads to a number of ways to find the optimal solution, the most naive of which is to check the cost at each extreme point and whichever is lowest ... Simplex Method Step 4: Calculate zj Row for New Tableau • For each column j, multiply the objective function coefficients of the basic variables by the corresponding numbers in column j and sum them. Simplex Method Step 5: Calculate cj-zj Row for New Tableau • For each column j, subtract the zj row from the cj row.Solution Help. Dual simplex method calculator. 1. Find solution using dual simplex method. Minimize Z = 2x1 + 3x2 + 0x3. subject to the constraints. 2x1 - x2 - x3 ≥ 3.Mar 13, 2015 · This paper proposes a streamlined form of simplex method which provides some great benefits over traditional simplex method. For instance, it does not need any kind of artificial variables or artificial constraints; it could start with any feasible or infeasible basis of an LP. This method follows the same pivoting sequence as of simplex phase 1 without showing any explicit description of ... Linear programming solver with up to 9 variables. New constraints could be added by using commas to separate them. Send feedback | Visit Wolfram|Alpha free app to track phone without them knowing
Guideline to Simplex Method Step1. Check if the linear programming problem is a standard maximization problem in standard form, i.e., if all the following conditions are satisfied: It’s to maximize an objective function; All variables should be non-negative (i.e. ≥ 0). Constraints should all be ≤ a non-negative. Step 2.Step-by-Step Examples. Algebra. Systems of Equations. Minimize the Equation given the Constraints. 3(x + 2) = 7y 3 ( x + 2) = 7 y , x + y > −1 x + y > - 1. Introduce slack variables u u and v v to replace the inequalities with equations. x+y− Z= −1 x + y - Z = - 1. 3x+6− 7y = 0 3 x + 6 - 7 y = 0. Subtract 6 6 from both sides of the ... The Simplex method is an approach to solving linear programming models by hand using slack variables, tableaus, and pivot variables as a means of finding the optimal solution of an optimization problem. linear-programming operations-research simplex-algorithm simplex-method. Updated on Jul 31, 2020. Python. Linear programming solver with up to 9 variables. New constraints could be added by using commas to separate them. Send feedback | Visit Wolfram|AlphaThe procedure to use the linear programming calculator is as follows: Step 1: Enter the objective function, constraints in the respective input field. Step 2: Now click the button “Submit” to get the optimal solution. Step 3: Finally, the best optimal solution and the graph will be displayed in the new window. Use of this system is pretty intuitive: Press "Example" to see an example of a linear programming problem already set up. Then modify the example or enter your own linear programming problem in the space below using the same format as the example, and press "Solve." Notes. Do not use commas in large numbers. For instance, enter 100,000 as 100000. Row operation calculator: v. 1.25 PROBLEM TEMPLATE: Interactively perform a sequence of elementary row operations on the given m x n matrix A. SPECIFY MATRIX DIMENSIONS:Simplex method calculator 1. Find solution using simplex method. Maximize Z = 3x1 + 5x2 + 4x3 subject to the constraints 2x1 + 3x2 ≤ 8 2x2 + 5x3 ≤ 10 3x1 + 2x2 + 4x3 ≤ 15 and x1, x2, x3 ≥ 0 2. Find solution using simplex method. Maximize Z = 4x1 + 3x2 subject to the constraints 2x1 + x2 ≤ 1000 x1 + x2 ≤ 800 x1 ≤ 400 x2 ≤ 700 and ...As described, the primal simplex method works with primal feasible, but dual infeasible (nonoptimal) bases. At the final (optimal) solution, the basis is both primal and dual feasible. Throughout the process we maintain primal feasibility and drive toward dual feasibility. In this section, a variant of the primal approach, known as the dual simplexThat is accomplished by a method due to C. E. Lemke [ ] which is ucually called the dual simplex method. We shall rst describe it as a mirror image of the simplex method and then we shall illustrate it on the example (1). Only then we shall note (without proof) that the dual simplex method is nothing but a disguised simplex method working on ... woodstock 1969 photos
The simplex method is an algorithm for solving linear programming problems. It is based on the fact that an optimal solution to a linear programming problem always lies at an extreme point. This fact leads to a number of ways to find the optimal solution, the most naive of which is to check the cost at each extreme point and whichever is lowest ...Solution Help. Dual simplex method calculator. 1. Find solution using dual simplex method. Minimize Z = 2x1 + 3x2 + 0x3. subject to the constraints. 2x1 - x2 - x3 ≥ 3. A “Simplex Method Calculator” is a specific type of calculator or software that solves linear programming problems using the simplex method. The simplex method is a widely used algorithm for solving linear programming problems. Example: Suppose you have a linear programming problem with multiple variables and constraints. By using a simplex ...The elements of the Q column are calculated by dividing the values from column P by the value from the column corresponding to the variable that is entered in the basis: Q 1 = P 1 / x 1,6 = 245 / -0.3 = -816.67; Q 2 = P 2 / x 2,6 = 225 / 0 = ∞; Q 3 = P 3 / x 3,6 = 140 / 0.4 = 350;Simplex Method Calculator - application which is help to find the optimal solution to the linear programming problem by the simplex method. Updated on. Jun 9, 2021.This JavaScript Works Well in Netscape Navigator Version 4 (such as 4.7). If this is not feasible for you, you may download (free-of-charge) a software package that solves Linear Programs models by the Simplex Method and/or the Push-and-Pull Method: Simplex on line Calculator is a on line Calculator utility for the Simplex algorithm and the two-phase method, enter the cost vector, the matrix of constraints and the objective function, execute to get the output of the simplex algorithm in linar programming minimization or maximization problems The Simplex algorithm is a popular method for numerical solution of the linear programming problem. The algorithm solves a problem accurately within finitely many steps, ascertains its insolubility or a lack of bounds. It was created by the American mathematician George Dantzig in 1947. Instructions. This pivot tool can be used to solve linear programming problems. By default, problems are assumed to have four variables and three constraints. To solve a problem of a different size, edit the two text fields to specify the number of rows and columns you want. You can enter data elements into each text field to define a specfic ...watch twilight movie
Simplex Algorithm Calculator is an online application on the simplex algorithm and two phase method. Inputs Simply enter your linear programming problem as follows 1) Select if the problem is maximization or minimization 2) Enter the cost vector in the space provided, ie in boxes labeled with the Ci. This JavaScript Works Well in Netscape Navigator Version 4 (such as 4.7). If this is not feasible for you, you may download (free-of-charge) a software package that solves Linear Programs models by the Simplex Method and/or the Push-and-Pull Method:Game theory. Matrix game solution by linear programming method. Complete, detailed, step-by-step description of solutions. Hungarian method, dual simplex, matrix games, potential method, traveling salesman problem, dynamic programmingFeb 21, 2019 · We will use this function to convert the equational form to the tableau. def to_tableau(c, A, b): xb = [eq + [x] for eq, x in zip(A, b)] z = c + [0] return xb + [z] to_tableau. In the next function, we check where nonbasic values can be increased without making the objective function value smaller. Finding the optimal solution to the linear programming problem by the simplex method. Complete, detailed, step-by-step description of solutions. Hungarian method, dual simplex, matrix games, potential method, traveling salesman problem, dynamic programmingThe simplex method is an algorithm for solving linear programming problems. It is based on the fact that an optimal solution to a linear programming problem always lies at an extreme point. This fact leads to a number of ways to find the optimal solution, the most naive of which is to check the cost at each extreme point and whichever is lowest ...Ch 6. Linear Programming: The Simplex Method Simplex Tableau The simplex method utilizes matrix representation of the initial system while performing search for the optimal solution. This matrix repre-sentation is called simplex tableau and it is actually the augmented matrix of the initial systems with some additional information.LP Simplex and dual Simplex method choose . precondition: Add solver: Load the Solver Add-in in Excel. Calculate: Define and solve a problem by using Solver / Example of a Solver evaluation . To repoduce: Open MS Excel; On the Data tab, in the Analysis group, click Solver; On select a solving method: choose LP Simplex; insert valid parameters ...Finding the optimal solution to the linear programming problem by the simplex method. Complete, detailed, step-by-step description of solutions. Hungarian method, dual simplex, matrix games, potential method, traveling salesman problem, dynamic programming Minimization by the Simplex Method. Set up the problem. Write a matrix whose rows represent each constraint with the objective function as its bottom row. Write the transpose of this matrix by interchanging the rows and columns. Now write the dual problem associated with the transpose. Solve the dual problem by the simplex method learned in ...Linear programming solver with up to 9 variables. New constraints could be added by using commas to separate them. Send feedback | Visit Wolfram|AlphaSimplex Method Step 4: Calculate zj Row for New Tableau • For each column j, multiply the objective function coefficients of the basic variables by the corresponding numbers in column j and sum them. Simplex Method Step 5: Calculate cj-zj Row for New Tableau • For each column j, subtract the zj row from the cj row. Finding the optimal solution to the linear programming problem by the simplex method. Complete, detailed, step-by-step description of solutions. Hungarian method, dual simplex, matrix games, potential method, traveling salesman problem, dynamic programmingThe 'interior-point-legacy' method is based on LIPSOL (Linear Interior Point Solver, ), which is a variant of Mehrotra's predictor-corrector algorithm , a primal-dual interior-point method. A number of preprocessing steps occur before the algorithm begins to iterate.The elements of the Q column are calculated by dividing the values from column P by the value from the column corresponding to the variable that is entered in the basis: Q 1 = P 1 / x 1,6 = 245 / -0.3 = -816.67; Q 2 = P 2 / x 2,6 = 225 / 0 = ∞; Q 3 = P 3 / x 3,6 = 140 / 0.4 = 350;statbotics
2.1 Simplex method: 1. Use the simplex method to solve the following LP problem. Maximize Z = 3x1 + 5x2 + 4x3 subject to the constraints 2x1 + 3x2 ≤ 8 2x2 + 5x3 ≤ 10 3x1 + 2x2 + 4x3 ≤ 15 and x1, x2, x3 ≥ 0 2. Use the simplex method to solve the following LP problem.Oct 5, 2021 · Introduction. Simplex algorithm (or Simplex method) is a widely-used algorithm to solve the Linear Programming (LP) optimization problems. The simplex algorithm can be thought of as one of the elementary steps for solving the inequality problem, since many of those will be converted to LP and solved via Simplex algorithm. [1] Two-Phase Simplex Method Calculator. The calculator given here can easily solve the problems related to the simplex method, two-phase method, and the graphical method as well. In this calculator, you can enter a limitless number of variables or constants.As described, the primal simplex method works with primal feasible, but dual infeasible (nonoptimal) bases. At the final (optimal) solution, the basis is both primal and dual feasible. Throughout the process we maintain primal feasibility and drive toward dual feasibility. In this section, a variant of the primal approach, known as the dual simplex This JavaScript Works Well in Netscape Navigator Version 4 (such as 4.7). If this is not feasible for you, you may download (free-of-charge) a software package that solves Linear Programs models by the Simplex Method and/or the Push-and-Pull Method:The simplex algorithm can be easily performed in TI Nspire CX and also in the TI-84 series. A program is created to provide an intuitive means to construct the initial tableau. The function prototype takes two arguments, one for a list of expression consisting the constraint inequalities plus the function to maximize (assumed to be the last in ...Game theory. Matrix game solution by linear programming method. Complete, detailed, step-by-step description of solutions. Hungarian method, dual simplex, matrix games, potential method, traveling salesman problem, dynamic programmingx 1, x 2 ≥ 0. Now, we can solve the linear programming problem using the simplex or the two phase method if necessary as we have seen in sections of theory In this case we use our famous calculator usarmos linear programming problems simplex method calculator. We placed each of the steps, first introduce the problem in the program. Step 1 ... Jan 16, 2018 · LP Simplex and dual Simplex method choose . precondition: Add solver: Load the Solver Add-in in Excel. Calculate: Define and solve a problem by using Solver / Example of a Solver evaluation . To repoduce: Open MS Excel; On the Data tab, in the Analysis group, click Solver; On select a solving method: choose LP Simplex; insert valid parameters ... Simplex on line Calculator is a on line Calculator utility for the Simplex algorithm and the two-phase method, enter the cost vector, the matrix of constraints and the objective function, execute to get the output of the simplex algorithm in linar programming minimization or maximization problems Simplex Method Calculator – Two Phase Online 🥇 . Find the optimal solution step by step to linear programming problems with our simplex method online calculator. ...Step-by-Step Examples. Algebra. Systems of Equations. Minimize the Equation given the Constraints. 3(x + 2) = 7y 3 ( x + 2) = 7 y , x + y > −1 x + y > - 1. Introduce slack variables u u and v v to replace the inequalities with equations. x+y− Z= −1 x + y - Z = - 1. 3x+6− 7y = 0 3 x + 6 - 7 y = 0. Subtract 6 6 from both sides of the ...As described, the primal simplex method works with primal feasible, but dual infeasible (nonoptimal) bases. At the final (optimal) solution, the basis is both primal and dual feasible. Throughout the process we maintain primal feasibility and drive toward dual feasibility. In this section, a variant of the primal approach, known as the dual simplexjacksonville fl zip codeLa calculadora Metodo Simplex online que aquí te presentamos permite resolver cualquier tipo de problemas de programacion lineal mediante el uso del método simplex. Para usarla solo debes seguir los siguientes pasos: Si alguna de las variables están restringidas a tomar solo números enteros, deberás indicarlo como una restricción ...modi method (optimal solution) calculator - Finding solution of Transportion problem using modi method (optimal solution), step-by-step online We use cookies to improve your experience on our site and to show you relevant advertising.The simplex method begins at a corner point where all the main variables, the variables that have symbols such as x1 x 1, x2 x 2, x3 x 3 etc., are zero. It then moves from a corner point to the adjacent corner point always increasing the value of the objective function. In the case of the objective function Z = 40x1 + 30x2 Z = 40 x 1 + 30 x 2 ...May 31, 2015 · Pivot a simplex tableau. Rows: Columns: Display tableau entries as. fractions. decimals with at most exactly digits after the decimal point. Last updated 31 May 2015. Please send comments, suggestions, and bug reports to Brian Kell < [email protected] >. Use of this utility is quite intuitive. Look at the spreadsheet layout below. The left-most column is for typing in row operations (optional; see the instructions) and the rest of it is for you to enter your matrix. Enter entries in the blank cells in fraction or decimal form, starting at the top left. Use the enter or tab to advance to the ...The Simplex Algorithm whose invention is due to George Dantzig in 1947 and in 1975 earned him the National Medal of Science is the main method for solving linear programming problems. The simplex algorithm performs iterations into the extreme points set of feasible region, checking for each one if Optimalit criterion holds.The Simplex Algorithm whose invention is due to George Dantzig in 1947 and in 1975 earned him the National Medal of Science is the main method for solving linear programming problems. The simplex algorithm performs iterations into the extreme points set of feasible region, checking for each one if Optimalit criterion holds.The Simplex algorithm is a popular method for numerical solution of the linear programming problem. The algorithm solves a problem accurately within finitely many steps, ascertains its insolubility or a lack of bounds. It was created by the American mathematician George Dantzig in 1947. Simplex Method Calculator – Two Phase Online 🥇 . Find the optimal solution step by step to linear programming problems with our simplex method online calculator. ...Jul 18, 2022 · 4.3: Minimization By The Simplex Method. In this section, we will solve the standard linear programming minimization problems using the simplex method. The procedure to solve these problems involves solving an associated problem called the dual problem. The solution of the dual problem is used to find the solution of the original problem. In solving this problem, we will follow the algorithm listed above. STEP 1. Set up the problem. Write the objective function and the constraints. Since the simplex method is used for problems that consist of many variables, it is not practical to use the variables x, y, z etc. We use symbols x1, x2, x3, and so on. Let.Nov 3, 2022 · The Simplex method calculator is a powerful and fast solution algorithm. It is an iterative method that uses the simplex method repeatedly until an optimal solution has been found. A Simplex method calculator can be constructed in many ways, including in spreadsheet form, text, flowchart, or computer program. 1.2 The Simplex Method The Simplex Method describes a method for entering inequalities as equations into a matrix and the keys to row-reduce that matrix. This method also is applicable to any number of independent variables, making graphing unnecessary. The following is a demonstration of an activity, including calculator commands, which make ... LP Simplex and dual Simplex method choose . precondition: Add solver: Load the Solver Add-in in Excel. Calculate: Define and solve a problem by using Solver / Example of a Solver evaluation . To repoduce: Open MS Excel; On the Data tab, in the Analysis group, click Solver; On select a solving method: choose LP Simplex; insert valid parameters ...pima federal credit union
Simplex Method Calculator – Two Phase Online 🥇 . Find the optimal solution step by step to linear programming problems with our simplex method online calculator. ...Roughly speaking, the idea of the simplex method is to represent an LP problem as a system of linear equations, and then a certain solu-tion (possessing some properties we will de ne later) of the obtained system would be an optimal solution of the initial LP problem (if any exists). The simplex method de nes an e cient algorithm of nding Feb 21, 2019 · We will use this function to convert the equational form to the tableau. def to_tableau(c, A, b): xb = [eq + [x] for eq, x in zip(A, b)] z = c + [0] return xb + [z] to_tableau. In the next function, we check where nonbasic values can be increased without making the objective function value smaller. Simplex Method Calculator – Two Phase Online 🥇 . Find the optimal solution step by step to linear programming problems with our simplex method online calculator. ...That's why at PM Calculators we have created a Simplex Method Calculator Online, which will allow you to develop maximization and minimization problems by applying the traditional simplex method and the two-phase method when applicable. Our tool has a friendly and easy to use design. The simplex method assumes that all variables are nonnegative, so there is no need to enter inequalities like x>=0,y>=0, etc. (Including them just makes all the tableaus bigger and can slow things down.) Decimal mode displays all the tableaus (and results) as decimals, rounded to the number of significant digits you select (up to 13).Simplex Method Calculator. The simplex method is universal. It allows you to solve any linear programming problems. Тhe solution by the simplex method is not as difficult as it might seem at first glance. This calculator only finds a general solution when the solution is a straight line segment.4.3: Minimization By The Simplex Method. In this section, we will solve the standard linear programming minimization problems using the simplex method. The procedure to solve these problems involves solving an associated problem called the dual problem. The solution of the dual problem is used to find the solution of the original problem.ava credit card
Jul 18, 2022 · Minimization by the Simplex Method. Set up the problem. Write a matrix whose rows represent each constraint with the objective function as its bottom row. Write the transpose of this matrix by interchanging the rows and columns. Now write the dual problem associated with the transpose. Solve the dual problem by the simplex method learned in ... Finding the optimal solution to the linear programming problem by the simplex method. Complete, detailed, step-by-step description of solutions. Hungarian method, dual simplex, matrix games, potential method, traveling salesman problem, dynamic programmingThe Simplex algorithm is a popular method for numerical solution of the linear programming problem. The algorithm solves a problem accurately within finitely many steps, ascertains its insolubility or a lack of bounds. It was created by the American mathematician George Dantzig in 1947. Get the variables using the columns with 1 and 0s. All other variables are zero. The maximum value you are looking for appears in the bottom right hand corner. Exercise 3.4.1 3.4. 1. 1. Use simplex method to solve: Maximize: P = 5x + 7y + 9z P = 5 x + 7 y + 9 z. Subject to: Row operation calculator: v. 1.25 PROBLEM TEMPLATE: Interactively perform a sequence of elementary row operations on the given m x n matrix A. SPECIFY MATRIX DIMENSIONS:Step-by-Step Examples. Algebra. Systems of Equations. Minimize the Equation given the Constraints. 3(x + 2) = 7y 3 ( x + 2) = 7 y , x + y > −1 x + y > - 1. Introduce slack variables u u and v v to replace the inequalities with equations. x+y− Z= −1 x + y - Z = - 1. 3x+6− 7y = 0 3 x + 6 - 7 y = 0. Subtract 6 6 from both sides of the ...