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To solve a system of equations in Excel, you can use the built-in Solver tool. To do this, enter your equations into the worksheet, and then select the Solver tool from the Data tab. In the Solver Parameters dialog box, enter your equations as the objective and the cells containing the equation as the changing cells. After clicking Solve, the solution will show up in the cells you specified. As an example, if you had the equations x+y=7 and x-y=3, you could enter these into the cells A1 and B1, respectively, and select the cells A2 and B2 as the changing cells. The solutions, x=5 and y=2, would then show up in cells A2 and B2 after clicking Solve.
To solve a system of equations in Excel, we can use the MMULT and MINVERSE functions.
The following examples show how to use these functions to solve several different systems of equations in Excel.
Example 1: Solve System of Equations with Two Variables
Suppose we have the following system of equations and we’d like to solve for the values of x and y:
5x + 4y = 35
2x + 6y = 36
To solve this system of equations, we can first type in the following values in Excel:
We can then use the following formula to solve for the values of x and y:
=MMULT(MINVERSE(A1:B2),C1:C2)
We can type this formula into cell E1 and then press CTRL + SHIFT + ENTER:
This tells us that the value for x is 3 and the value for y is 5.
Example 2: Solve System of Equations with Three Variables
Suppose we have the following system of equations and we’d like to solve for the values of x, y, and z:
4x + 2y + 1z = 34
3x + 5y – 2z = 41
To solve this system of equations, we can first type in the following values in Excel:
We can then use the following formula to solve for the values of x, y, and z:
=MMULT(MINVERSE(A1:C3),D1:D3)
We can type this formula into cell F1 and then press CTRL + SHIFT + ENTER:
This tells us that the value for x is 5,the value for y is 6, and the value for z is 2.
Example 3: Solve System of Equations with Four Variables
Suppose we have the following system of equations and we’d like to solve for the values of w, x, y, and z:
6w + 2x + 2y + 1z = 37
2w + 1x + 1y + 0z = 14
3w + 2x + 2y + 4z = 28
2w + 0x + 5y + 5z = 28
To solve this system of equations, we can first type in the following values in Excel:
We can then use the following formula to solve for the values of w, x, y, and z:
=MMULT(MINVERSE(A1:D4),E1:E4)
We can type this formula into cell G1 and then press CTRL + SHIFT + ENTER:
This tells us that the value for w is 4, x is 3, y is 3, and z is 1.