**Ex:** This example describes how to solve a set of three linear equations with three variables. Here’s an example of a set of linear equations:

4x + y -2z =0

2x – 3y +3z =9

-6x -2y +z = 0

The question that Solver will answer is What values of x, y, and z satisfy all three equations?

**Let’s Understand the solution.**

The following image shows a workbook set up to solve this problem. This workbook has three named cells,

which makes the formulas more readable:

x: C11

y: C12

z: C13

The three named cells are all initialized to 1 (which certainly doesn’t solve the equations).

Solver will attempt to solve this series of linear equations.

The three equations are represented by formulas in the range B6:B8:

B6: =(4*x)+(y)-(2*z)

B7: =(2*x)-(3*y)+(3*z)

B8: =-(6*x)-(2*y)+(z)

These formulas use the values in the x, y, and z named cells. The range C6:C8 contains the

“desired” result for these three formulas.

Solver will adjust the values in x, y, and z — that is, the changing cells in C11:C13 — subject to

these constraints:

B6=C6

B7=C7

B8=C8

Note: This problem doesn’t have a target cell because it’s not trying to maximize or minimize anything. However, the Solver Parameters dialog box insists that you specify a formula for the Set Target Cell field. Therefore, just enter a reference to any cell that has a formula.

The following image shows the solution. The x (0.75), y (–2.0), and z (0.5) values satisfy all three equations.

Hope, this helped you. Feel free to drop a comment or mail.

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