We have the following **three** equations.

**2x + 5y + 2z = -38
**

**3x – 2y + 4z = 17**

**-6x + y – 7z = -12**

We’ll determine the value of the three variables,

**x**,

**y**, and

**z**.

### Method 1 – Applying Cramer’s Rule to Solve Algebraic Equations with Multiple Variables in Excel

** Steps:**

- Write down the equations in cells in the
**B5:B7**range.

- Make a simple data range like in the image below. In cells in the
**C11:E13**range, we inserted the**Coefficients**of the variables**x**,**y**, and**z**. In cells in the**F11:F13**range, we input the**Constants**.

- Select cell
**C15**and put in the following formula.

`=C11`

- Press the
**Enter**key.

- Drag the
**Fill Handle**tool up to cell**E17**both vertically and horizontally.

- Select the cells in the
**C15:E17**range. - Press
**Ctrl + 1**.

- This opens the
**Format Cells**dialog box. - Move to the
**Border**tab. - Select the
**Style**as shown in the picture below. - Choose two outside borders like in the image.
- Click
**OK**.

- The data range looks like a determinant.

- Select cell
**C19**and insert the following formula.

`=F11`

- Press
**Enter**. We’re putting the**Constants**in the first column.

*Note:** In D*

_{x}*, constants will sit in the first column. The coefficients of*.

**y**and**z**will occupy the next two columns- Put the coefficients of
**y**and**z**in the next two columns.

- In
**D**, the constants will sit in the second column. The other two columns are occupied by the coefficients of_{y}**x**and**z,**respectively.

- In
**D**, the constants will sit in the third column. The other two columns are occupied by the coefficients of_{z}**x**and**y,**respectively.

- Select cell
**D16**and put the following formula in the**Formula Bar**.

`=MDETERM(C15:E17)`

**The MDETERM function** determines the determinant of an array.

- Press
**Enter**.

The determinant is **-13**.

**Similarly**, calculate the determinant of**Dx**,**Dy**, and**Dz**.

- Select cell
**G5**and paste the formula below.

`=G20/G16`

- Press
**Enter**.

That’s how we get the value of variable **x**.

**Similarly**, find the value of**y**and**z**by dividing their determinant (**D**_{y; }**D**) with the determinant_{z}**D,**respectively.

**Read More:** How to Solve an Equation for X When Y is Given in Excel

### Method 2 – Utilizing MINVERSE and MMULT Functions

** Steps:**

- Create a simple data range containing the
**Coefficients**and**Constants**of the three equations like Method 1.

- Create the matrix
**A**and matrix**B**as in the image below. The matrix**A**contains the*coefficients*of the variables. The matrix**B**includes the*constants*of the equations.

- Create a space for the inverse matrix of
**A**.

- Select cell
**C19,**which is the first cell in this area, and enter the following:

`=MINVERSE(C15:E17)`

**The MINVERSE function** returns the inverse matrix of a matrix. The main matrix should be stored in an array.

- Press
**Enter**.

*Note:** If you are using any other version of Excel rather than Microsoft Excel 365, make sure to press CTRL+SHIFT+ENTER to get the result*.

- Select cell
**G5**and paste in the following formula:

`=MMULT(C19#,H15:H17)`

The** MMULT **function multiplies two matrices in array form. Then, it returns the product in an array form.

- Hit the
**Enter**key.

We get the values of the variables in cells in the **G5:G7** range.

**Read More:** How to Solve 2 Equations with 2 Unknowns in Excel

### Method 3 – Using the Solver Add-in to Solve Algebraic Equations with Multiple Variables in Excel

** Steps:**

- Create a basic outline like in the image below, as in Method 1.

- Construct a data range like the one below. It should contain the headings
**R.H.S**and**L.H.S**horizontally and**Equation 1**,**Equation 2**, and**Equation 3**vertically.

- Go to the
**File**tab.

- Select
**Options**from the menu.

- The
**Excel Options**window opens up. - Move to the
**Add-ins**menu. - Select
**Excel Add-ins**from the**Manage**drop-down list. - Click on
**Go**.

- This opens the
**Add-ins**dialog box. - Check the box for
**Solver Add-in**. - Click
**OK**.

- Create a data range like the picture below.

- Select cell
**C16**and insert the following formula:

`=SUMPRODUCT(C11:E11,C21:E21)`

The** SUMPRODUCT **function returns the sum of the products of the corresponding values from all the arrays. It takes one or more arrays as an argument, multiplies the corresponding values of all the arrays, and then returns the sum of the products.

- Hit the
**Enter**key on your keyboard.

*Note:** For your convenience, we highlighted the cell ranges of the arguments in the picture above*.

- Put the
*constant*of**Equation 1**in cell**E16**.

**Equivalently**, fill up the fields of**Equation 2**and**Equation 3**.

- Jump to the
**Data**tab. - Select
**Solver**in the**Analyze**group.

- The
**Solver Parameters**wizard opens. - Put cell
**C16**in the**Set Objective**box. - Put the cells in the
**C21:E21**range in the**By Changing Variable Cells**box. - Click on the
**Add**button.

- This opens the
**Add Constraint**input box. - Give the reference of cell
**C16**into the**Cell Reference**box. - Select the equal sign (
**=**). - Give the cell reference of cell
**E16**into the**Constraint**box. - Click on
**Add**.

- Repeat the above steps for
**Equation 2**and**Equation 3**. - Click on the
**OK**button.

- This returns us to the
**Solver Parameters**window. - Untick the box for
**Make Unconstrained Variables Non-Negative**. - Choose
**Simplex LP**from the**Select a Solving Method**drop-down list. - Click on
**Solve**.

- The
**Solver Results**wizard will open. - Select the
**OK**button.

- We can see the values of the variables in cells in the
**C21:E21**range.

- Move the answers to the top of the sheet to make them visible. We transferred them to the cells in the
**G5:G7**range.

**Read More: **How to Solve System of Equations in Excel

**Practice Section**

We have provided a Practice section like below in each sheet on the right side.

Read More: How to Solve Polynomial Equation in Excel

**Download the Practice Workbook**

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