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How to Solve System of Equations in Excel (2 Easy Methods)

Are you finding ways to solve the system of linear equations in Excel and searching for the easiest guide? Then I think you have come to the right place. In this article, I’ll show 2 easy and useful methods to solve the system of equations in Excel with sharp steps.


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2 Ways to Solve System of Equations in Excel

Here’s the dataset that we’ll use to explore the methods, it has three equations of three variables.

How to Solve System of Equations in Excel


1. Using MINVERSE and MMULT Functions to Solve System of Equations

First, we’ll apply the MINVERSE and MMULT functions to solve the equations. For that, I have placed the variables of x, y, and z in a matrix- A and the constraints in the matrix- B.

Using MINVERSE and MMULT Functions to Solve System of Equations

According to matrix notation, we know that we can write: AX = B. here, X is the matrix of the unknown variables.

So to find X, we can write X = A‾ ¹B. Now let’s find A‾ ¹ first.

Using MINVERSE and MMULT Functions to Solve System of Equations

Steps:

  • First, select the empty cells of the A‾ ¹
  • Then write the following formula in the formula bar-
=MINVERSE(C9:E11)
  • Next, hit the ENTER button just. You may have to press CTRL + SHIFT + ENTER in the earlier versions of excel as it is an array formula.

Then soon after you will get the inverse matrix like the image below.

Using MINVERSE and MMULT Functions to Solve System of Equations

Now it’s time for the final operation to find the variables.

  • Select the cells of the X matrix.
  • After that type the following formula in the formula bar-
=MMULT(C13:E15,H9:H11)
  • Finally, just press the ENTER button to finish. Here also, you may have to press CTRL + SHIFT + ENTER in the earlier versions of excel as it is an array formula.

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


Similar Readings


2. Applying Excel Solver Add-in to Solve System of Equations

There’s another smart way to solve the system of equations in excel, which is using an Add-in of Excel. Excel has an Add-in named Solver which can easily solve the system of equations. And it’s quite helpful for a large number of equations. First, we’ll activate the Solver Add-in. If you know how to activate then skip these steps.

Steps:

  • Click on the File tab beside the Home tab.

Applying Excel Solver Add-in to Solve System of Equations

  • Next from the appeared menu, select Options.

Applying Excel Solver Add-in to Solve System of Equations

  • Click on Add-ins.
  • Later, select Excel Add-ins from the Manage box and then press Go.

Applying Excel Solver Add-in to Solve System of Equations

  • From the available list, mark Solver Add-in.
  • Then just press OK.

Applying Excel Solver Add-in to Solve System of Equations

Soon after, you will get the Solver Add-in available in the Analyze section of the Data tab.

Applying Excel Solver Add-in to Solve System of Equations

Now we’ll insert the L.H.S (Left Hand Side) of the equations in column C and R.H.S (Right Hand Side) of the equation in column D. While inserting L.H.S, we’ll use the cell reference of the variables x,y, and z.

  • For the first equation type =1*E10+2*E11-1*E12 in Cell C10.

Applying Excel Solver Add-in to Solve System of Equations

  • Insert =2*E10+1*E11+2*E12 in Cell C11.

Applying Excel Solver Add-in to Solve System of Equations

  • And write =3*E10+1*E11+4*E12 in Cell C12.

These formulas will return 0 as cells of x,y, and z are still empty, which means zero.

Applying Excel Solver Add-in to Solve System of Equations

  • After that, insert the constraints manually in column D.

Applying Excel Solver Add-in to Solve System of Equations

  • Now it’s time to apply the Solver Add-in. Click as follows: Data > Solver.

Applying Excel Solver Add-in to Solve System of Equations

Soon you will get a dialog box like this named- Solver Parameters.

  • From the Set Objective box, click on the Open icon.

Applying Excel Solver Add-in to Solve System of Equations

  • Select Cell C10 and hit the ENTER button.

  • Next, mark the Max option and again click on the open icon from the By Changing Variable Cells box.

Applying Excel Solver Add-in to Solve System of Equations

  • Select the range from the variable column and press the ENTER button.

At this moment we’ll add three subjects to the constraints.

  • Click on the Add button.

  • For the first equation, select Cell C10 in the Cell Reference box, choose the equal sign from the drop-down list, and select Cell D10 in the Constraint box.
  • Then just press OK.

We are done with the first equation.

  • Again press Add button and do the same operations for the rest of the two equations.
  • Next, unmark the Make Unconstrained Variables Non-Negative option and press Solve.

  • Then from the Solver Results dialog box, mark Keep Solver Solution and press OK.

Now take a look, we got the same output as our first method.

Read More: How to Insert Equation in Excel (3 Easy Ways)


Conclusion

That’s all for the article. I hope the procedures described above will be good enough to solve the system of equations in Excel. Feel free to ask any question in the comment section and please give me feedback.


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Mithun

Mithun

Hello! I am Md. Sourov Hossain Mithun. Welcome to my profile. Currently, I am working at Exceldemy as an Excel and VBA Content Developer. Excel is amazing software. Here I will post excel related useful articles. I am a graduate of Bangladesh University of Engineering and Technology. I love to learn new things and work with them. Thank you.

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