Need to learn **how to solve algebraic equations with multiple variables** in Excel? If you are looking for such unique tricks, youâ€™ve come to the right place. Here, we will take you through **3** easy and effective methods of solving algebraic equations with multiple variables.

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## Download Practice Workbook

You may download the following Excel workbook for better understanding and practice yourself.

## 3 Methods to Solve Algebraic Equations with Multiple Variables

Letâ€™s say we have the following **three** equations.**2x + 5y + 2z = -38**

**3x â€“ 2y + 4z = 17**

**-6x + y â€“ 7z = -12**

Now, weâ€™ll solve the equations by the following three methods. Thus, weâ€™ll determine the value of the three variables

**x**,

**y**, and

**z**.

Here, we have used

*Microsoft Excel 365*version, you may use any other version according to your convenience.

### 1. Applying Cramerâ€™s Rule to Solve Algebraic Equations with Multiple Variables in Excel

**Cramerâ€™s rule** is a particular formula in linear algebra. We often use it to solve systems of linear equations with as many equations as unknowns. It is effective whenever the equations have a distinct solution. Here, weâ€™ll execute the same process just in Excel. So, follow these simple steps.

**ðŸ“Œ**** Steps:**

- At the very beginning, write down the equations in cells in the
**B5:B7**range.

- Secondly, make a simple data range like in the image below.
- Here, in cells in the
**C11:E13**range, we insert the**Coefficients**of the variables**x**,**y**, and**z**. - Also, in cells in the
**F11:F13**range, we input the**Constants**. Actually, they are the right-hand sides of the equations.

- At this moment, select cell
**C15**and put in the following formula.

`=C11`

- Then, press the
**ENTER**key.

- In this instance, drag the
**Fill Handle**tool up to cell**E17**in two steps. Firstly, drag it vertically down. Then, move it horizontally to the right. - Thus, youâ€™ll get the
*coefficients*in these cells.

- Next, select cells in the
**C15:E17**range. - Later, press
**CTRL+1**.

- Suddenly, it opens the
**Format Cells**dialog box. - After that, move to the
**Border**tab. - Then, select the
**Style**as shown in the picture below. - Later, give two outside borders like in the image.
- Lastly, click
**OK**.

- Now, the data range looks like a determiner.

- Then, select cell
**C19**and write down the following formula.

`=F11`

- Then, press
**ENTER**. - Actually, here weâ€™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- At this time, 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 get occupied by the coefficients of_{y}**x**and**z**respectively.

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

- Then, select cell
**D16**and get the following formula in the**Formula Bar**.

`=MDETERM(C15:E17)`

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

- Now, press
**ENTER**.

So, the determinant is **-13**.

**Similarly**, calculate the determinant of**x**,**y**, and**z**also.

`=G20/G16`

- Hence, press
**ENTER**.

Thatâ€™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**

### 2. Utilizing MINVERSE and MMULT Functions

In this method, weâ€™ll use some Excel functions to solve the problem. Letâ€™s see the process in detail.

**ðŸ“Œ**** Steps:**

- First of all, create a simple data range containing the
**Coefficients**and**Constants**of the three equations like**Method 1**.

- Then, create matrix
**A**and matrix**B**as in the image below. - Here, matrix
**A**contains the*coefficients*of the variables. - On the other hand, matrix
**B**includes the*constants*of the equations.

- Afterward, create a space for the inverse matrix of
**A**.

- Then, select cell
**C19**which is the first cell in this area. - Later, write down the following formula.

`=MINVERSE(C15:E17)`

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

- Lastly, 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*.

- Eventually, select cell
**G5**and paste the following formula.

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

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

- Correspondingly, hit the
**ENTER**key.

Thus, we get the values of the variables in cells in the **G5:G7** range.

**Read More: How to Solve For x in Excel (2 Simple Ways)**

### 3. Using Solver Add-in to Solve Algebraic Equations with Multiple Variables in Excel

In this method, weâ€™ll use an add-in of Excel. Itâ€™s the **Solver** add-in. So, without further delay, letâ€™s dive in!

**ðŸ“Œ**** Steps:**

- Primarily, create a basic outline like in the image below. Also, we did it in
**Method 1**.

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

- Later, go to the
**File**tab.

- Then, select
**Options**from the menu.

- Instantly, the
**Excel Options**window opens up. - Then, move to the
**Add-ins**menu. - After that, select
**Excel Add-ins**from the**Manage**drop-down list. - Later, click on
**Go**.

- Immediately, it opens the
**Add-ins**dialog box. - Now, check the box of
**Solver Add-in**. - Lastly, click
**OK**.

- At this moment, create a data range like the picture below.

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

Here, 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.

- As always, tap the
**ENTER**key on your keyboard.

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

- After that, put the
*constant*of**Equation 1**in cell**E16**.

**Equivalently**, fill up the fields of**Equation 1**and**Equation 2**.

- Then, jump to the
**Data**tab. - Next, select
**Solver**on the**Analyze**group.

- Hence, the
**Solve Parameters**wizard opens. - Then, select cell
**C16**in the**Set Objective**box. - After that, select cells in the
**C21:E21**range in the**By Changing Variable Cells**box. - Lastly, click on the
**Add**button.

- Thus, it opens the
**Add Constraint**input box. - Later, give the reference of cell
**C16**into the**Cell Reference**box. - Next, select the equal sign (
**=**). - After that, give the cell reference of cell
**E16**into the**Constraint**box. - Lastly, click on
**Add**.

- Correspondingly, repeat the
**above steps**for**Equation 2**and**Equation 3**. - At last, click on the
**OK**button.

- Again, it returns us to the
**Solver Parameters**window. - Then, untick the box of
**Make Unconstrained Variables Non-Negative**. - After that, choose
**Simplex LP**from the**Select a Solving Method**drop-down list. - Lastly, click on
**Solve**.

- Hence, the
**Solver Results**wizard will open. - Here, select the
**OK**button.

- Thus, we can see the values of the variables in cells in the
**C21:E21**range.

- Finally, move the answers to the top of the sheet to make them visible easily.
- So, transfer them to cells in the
**G5:G7**range.

Thatâ€™s how we can solve these algebraic equations with multiple variables.

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

## Practice Section

For doing practice by yourself we have provided a **Practice** section like below in each sheet on the right side. Please do it by yourself.

## Conclusion

This article provides easy and brief solutions to solve algebraic equations with multiple variables in Excel. Donâ€™t forget to download the **Practice** file. Thank you for reading this article, we hope this was helpful. Please let us know in the comment section if you have any queries or suggestions. Please visit our website **Exceldemy** to explore more.

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