Excel is a popular and useful tool for analyzing data and solving mathematical equations. One such case where Excel shines is effortlessly solving simultaneous equations. Keeping this in mind, this article demonstrates 3 useful ways for solving simultaneous equations in Excel.

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## 3 Ways to Solve Simultaneous Equations in Excel

Say, we have the 2 linear equations that we want to solve for **X** and **Y**.

**3X – Y = 5**

**4X – Y = 2**

So, let’s see how we can solve simultaneous equations in Excel in order to obtain the values of *X *and *Y*.

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

__Method-1__: Utilizing MMULT and MINVERSE Functions

Let’s start with the most obvious method of solving simultaneous equations in Excel. Yes, you’re right. we’ll combine the **MMULT** and **MINVERSE** functions to obtain the values of *X* and *Y*. Therefore, let’s see it in action.

📌 ** Steps**:

- In the first place, select the
**D13:D14**cells and enter the following expression.

`=MMULT(MINVERSE(B9:C10),D9:D10)`

Here, the **B9:C10 **and **D9:D10** cells represent the *X* and *Y *coefficients and the constant values on the right-hand side of the equation.

📃 *Note: **Please make sure to press the CTRL + SHIFT + ENTER keys on your keyboard since this is an array formula.*

**Formula Breakdown:**

**MINVERSE(B9:C10)****→**returns the inverse matrix for the matrix stored in an array. Here, the function returns the values of the inverse matrix.**=MMULT(MINVERSE(B9:C10),D9:D10)→**returns the matrix product of two arrays. Here, the function multiplies the inverse matrix array with the values on the**RHS**and gives the output.

Finally, the results should look like the image shown below.

__Method-2__: Solving Simultaneous Equations with Excel Add-in

Another simple way to solve simultaneous equations in Excel involves using the **Solver Add-in**. It’s simple and easy, just follow along.

📌 ** Steps**:

- First and foremost, move to the
**C13**cell >> type in the**LHS**of the linear equation. In this case, the expression is given below.

`=3*D9-D10`

Here, the **D9 **and **D10 **cells indicate the **Initial Values** of *X* and *Y* respectively.

- Similarly, enter the second expression in the
**C14**cell.

`=4*D9-D10`

- Secondly, click the
**File**tab at the top-left corner.

- Now, click on
**Options**at the bottom of the window.

- Then, click the
**Add-ins**option >> select the**Solver Add-in**>> hit the**Go**button.

Now, this opens the **Add-ins** dialog box.

- In turn, choose the
**Solver Add-in**option >> click the**OK**button.

Finally, this adds the **Solver Add-in **in Excel.

- Thirdly, move to the
**Data**tab >> click on**Analyze**>> press the**Solver**option.

In an instant, the **Solver **window pops up.

- Now, at the
**Set Objective**field type in the**C13**cell. - Afterward, at the
**To**options select the**Value Of**option and enter the values of the constant, here, it is**5**. - Following this, at the
**By Changing Variable Cells**field, enter the**C8:C9**range of cells. - Subsequently, hit the
**Add**button to set the constraints.

Now, the **Add Constraint** wizard pops out.

- To begin with, enter the
**C13**cell reference at the**Cell Reference**field. - Next, choose an equal sign (
**=**) from the dropdown list >> type in the**D13**cell in the**Constraint**field >> hit the**Add**button.

- Then, repeat the same procedure to add a second constraint and click on
**OK**.

- In turn, choose the
**Simplex LP**option in the**Select a Solving Method**field. - Eventually, click the
**Solve**button.

- Additionally, insert a check on the
**Keep Solver Solution**option and click**OK**.

Consequently, the results should look like the screenshot shown below.

__Method-3__: Solve Simultaneous Equations with 3 Variables Applying Cramer’s Rule

**Cramer’s rule** is a formula in linear algebra for solving a system of linear equations with multiple unknowns. Here, we’ll employ *Cramer’s rule* to solve the 3 linear equations with 3 unknowns, so, just follow these simple steps.

📌 ** Steps**:

- Firstly, proceed to the
**C11**cell and enter the**C6**cell reference.

`=C6`

Here, the **C6 **cell points to the coefficient of *X*.

- Next, enter all the values as shown in the image below and press the
**CTRL + 1**button.

This opens the **Format Cells** wizard.

- Now, navigate to the
**Border**tab and follow the steps for the**Style**,**Outside Borders**as shown in the picture given below.

- Secondly, proceed to the
**C15**cell >> enter the values from the**RHS**column. - Following this, enter the coefficients of
**Y**and**Z**in the next two columns.

- In a similar fashion, enter the values for
**D**in the second column._{y}

- Similarly, repeat the same process for
**D**and enter it in the third column._{z}

- Now, jump to the
**G12**cell and enter the formula below.

`=MDETERM(C11:E13)`

In this expression, the **MDETERM** function calculates the determinant of the **C11:E13** array.

- Likewise, compute the determinants of x, y, and z.

- Finally, move to the
**I6**cell and enter the expression given below.

`=G16/G12`

Here, the **G16** and **G12 **cells represent the values **D**** _{x}** and

**D**respectively.

Subsequently, the output should look like the picture shown below.

## Solving Quadratic Equations in Excel

So far, we’ve discussed solving only linear equations, but you can also solve quadratic equations using the **Goal Seek** option in Excel. So, let’s begin.

📌 ** Steps**:

- Firstly, go to the
**E10**cell and type in the quadratic equation as shown below.

`=5*E9^2 - 4*E9 - 9`

Here, the **E9** cell refers to the values of *X*.

- Next, move to the
**Data**tab >> click the**What-If Analysis**drop-down >> select the**Goal Seek**option.

This opens the **Goal Seek** wizard.

- Now, in the
**Set cell**field, enter the**E10**cell >> next, in the**To value**field, type in**10**>> then, in the**By changing cell**option >> select the**E9**cell.

Lastly, your output should look like the screenshot given below.

## Solving Linear Equations in Excel Using Solver

For our last method, we’ll demonstrate how to solve linear equations with Excel’s **Solver Add-in**. Hence, let us see the process in detail.

📌 ** Steps**:

- Initially, navigate to the
**C15**cell and type in the linear equation as shown in the picture below.

`=3*D10-5*D11+D12`

Here, the **D10**, **D11**, and **D12** cells indicate the **Initial Values** of **X**, **Y**, and **Z**.

Likewise, repeat the same process for the other two equations.

- Secondly, navigate to the
**Data**tab >> click the**Analyze**drop-down >> choose the**Solver**option.

- Thirdly, follow the detailed steps described in
**Method 2**.

Eventually, your output should look like the image given below.

## Practice Section

We have provided a** Practice** section on the right side of each sheet so you can practice yourself. Please make sure to do it by yourself.

## Conclusion

I hope all of the methods mentioned above for solving simultaneous equations in Excel will prompt you to apply them more effectively. If you have any questions or feedback, please let me know in the comment section. Or you can check out our other articles related to Excel functions on this website.

Hi,

I am trying to solve linear equations with multiple unknowns. Sample below. Problem is I have only one equation with multiple unknows

19.6=a+0.0124x+0.0304y+0.175z

I need a excel function to give possible values for the variables in above equation. Anyone knows how to do it?

P.S: I am not looking for solutions where we have three unknowns and hence we cant solve with less than three questions. I need to know what are the possible (not unique) values that satisfies the above equation

Thanks

Need more lessons on solving quadratic and linear equations.

Very helpful! Thank You

thank you so much it was really helpful 😀

Glad to know that it helped you.

Thanks and regards

Kawser Ahmed