How to Solve 2 Equations with 2 Unknowns in Excel (2 Examples)

Method 1 – Combine MMULT and MINVERSE Functions

Steps:

Select the D13 and D14 cells.

Select Cells to Solve 2 Equations with 2 Unknowns in Excel

Insert the formula below to solve the equations:

=MMULT(MINVERSE(B8:C9),E8:E9)

Press Ctrl + Shift + Enter to get your desired result.

Combine MMULT and MINVERSE Functions to Solve 2 Equations with 2 Unknowns in Excel

Thus, your equations with two unknowns will be solved, and you will get the solutions in D13 and D14 cells. For example, the output should look like this.

Solved 2 Equations with 2 Unknowns in Excel

Note: Here, you must press Ctrl + Shift + Enter to get your desired result because it is an array formula. If you press Enter only, the formula won’t work properly, and you won’t get your proper result.

Method 2 – Use the Solver Add-In in Excel

Step 1: Installing Solver Add-In

Generally, Solver doesn’t remain in any tab initially. Rather, you need to add it from the Excel add-in section.

Go to the File tab.

Access the File Tab

Choose the Options option from the expanded File tab.

Choose the Options Option

The Excel Options window will appear.
Go to the Add-ins tab from the window >> select the Solver Add-in option >> click the Go… button.

Excel Options Window

The Add-ins window will appear now.
Tick the Solver Add-in option from the window and click the OK button.

Add-ins Window

Thus, the Solver tool will be added to the Data tab.

Solver Tool to Solve 2 Equations with 2 Unknowns in Excel

Step 2: Preparing the Dataset in Proper Format to Solve Functions

To calculate using the Solver tool, you will first need to assume the unknowns’ values and calculate the functions’ values.

Set the X and Y values as 1 and 1. As a result, the values of the functions would be 3 and 1. But the required values are 8 and 5.
Record these assumed values, calculated function values, and required values of the functions in the Excel file.

Prepared Dataset

Step 3: Using Solver to Get Results

Now, you can finally get the values of the two unknowns.

Go to the Data tab >> Solver tool.

Solver Tool to Solve 2 Equations with 2 Unknowns in Excel

The Solver Parameters window will appear.
At the Set Objective: text box, refer to cell C12.
At the To: options list, put the radio button on the Value Of: option and write 8 in the text box beside this option.
At the By Changing Variable Cells: text box, refer to C8:C9 cells.
To set the constraints, click the Add button at the Subject to the Constraints: group.

Solver Parameters Window

The Add constraint dialogue box will appear.
At the Cell Reference text box, refer to the C12 cell.
Choose equal sign (=) from the dropdown list and refer to the D12 cell in the Constraint: text box.
Click on the OK button.

Add Constraint Window

Repeat the previous 5 steps to add another equation’s constraint.
The Solver Parameters window will look like the following.
Choose the Simplex LP option from the Select a Solving Method: options.
Click on the Solve button.

Solve 2 Equations with 2 Unknowns in Excel using the Solver Tool

The Solver Results window will appear to inform you that a solution has been found.
Put the radio button on the Keep Solver Solution option and click on OK.

Solver Results Window

Your equations with 2 unknowns will be solved, and the following results will be shown in the C8:C9 cells. For instance, the result would look like this.

Solved 2 Equations with 2 Unknowns in Excel