*36*

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 weâ€™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 weâ€™d like to solve for the values of x, y, and z:

4x + 2y + 1z = 34

3x + 5y â€“ 2z = 41

2x + 2y + 4z = 30

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 weâ€™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**.

**Additional Resources**

The following tutorials explain how to perform other common operations in Excel:

How to Plot an Equation in Excel

How to Normalize Data in Excel

How to Fit a Curve in Excel