Tanjim Reza
Excel is a powerful tool and is very renowned for data analyzing and solving large calculations. In several mathematics problems and calculations, we need to solve 2 equations with 2 unknowns. Excel is very handy to use in this regard. If you are looking for ways to do this, you have landed in the perfect place. In this article, I will show you two effective methods to solve 2 equations with 2 unknowns in Excel.
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2 Methods to Solve 2 Equations with 2 Unknowns in Excel
Say, you have 2 equations with 2 unknowns x and y. The equations are as follows:
2x + y = 8
3x – 2y = 5
Now, you can follow any of the two methods given below to solve these equations.
1. Combine MMULT and MINVERSE Functions
The most effective and quickest method for solving two equations with 2 unknowns is to combine the MMULT and MINVERSE functions. Follow the steps below to do this.
📌 Steps:
- First and foremost, select the D13 and D14 cells.
- Following, insert the formula below to solve the equations.
=MMULT(MINVERSE(B8:C9),E8:E9)- Subsequently, press Ctrl + Shift + Enter to get your desired result.
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.
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.
Read More: How to Solve For x in Excel (2 Simple Ways)
Similar Readings
- How to Solve Polynomial Equation in Excel (5 Simple Methods)
- Solve Exponential Equation in Excel (4 Suitable Examples)
- How to Solve Differential Equation in Excel (With Easy Steps)
2. Using Solver Add-In in Excel
Another smart way to solve 2 equations with 2 unknowns is to use the Excel Solver add-in. Go through the steps below to accomplish this.
📌 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.
- In order to do this, first, you need to go to the File tab.
- Afterward, choose the Options option from the expanded File tab.
- At this time, the Excel Options window will appear.
- Now, go to the Add-ins tab from the window >> select the Solver Add-in option >> click on the Go… button.
- As a result, the Add-ins window will appear now.
- Following, tick the Solver Add-in option from the window and click on the OK button.
Thus, the Solver tool will be added to the Data tab.
📌 Step 2: Preparing the Dataset in Proper Format to Solve Functions
Now for calculating using the Solver tool, at first you will need to assume the unknowns’ values and calculate the functions’ values.
- To do this, we set the X and Y values as 1 and 1. As a result, the values of the functions would be 3 and 1 respectively. But the required values are 8 and 5.
- Now, record these assumed values and calculated function values, and required values of the functions in the Excel file.
📌 Step 3: Using Solver to Get Results
Now, you can finally get the values of the two unknowns.
- Initially, go to the Data tab >> Solver tool.
- As a result, the Solver Parameters window will appear.
- Now, at the Set Objective: text box, refer to cell C12.
- Afterward, At the To: options list put the radio button on the Value Of: option and write 8 at the text box beside this option.
- Following, at the By Changing Variable Cells: text box, refer to C8:C9 cells.
- Subsequently, for setting the constraints, click on the Add button at the Subject to the Constraints: group.
- Consequently, the Add constraint dialogue box will appear.
- At the Cell Reference text box, refer to the C12 cell.
- Following, choose equal sign (=) from the dropdown list and refer to the D12 cell in the Constraint: text box.
- Last but not least, click on the OK button.
- Repeat the previous 5 steps to add another equation’s constraint.
- Afterward, the Solver Parameters window will look like the following.
- Here, choose the Simplex LP option from the Select a Solving Method: options.
- Subsequently, click on the Solve button.
- As a result, the Solver Results window will appear informing you that it found a solution.
- Here, put the radio button on the Keep Solver Solution option and click on the OK button.
Consequently, 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.
Read More: How to Solve an Equation for X When Y is Given in Excel
Conclusion
To conclude, in this article, I have shown you 2 effective methods to solve two equations with two unknowns in Excel. I suggest you read the full article carefully and apply the knowledge to your needs. You can also download our free workbook to practice. I hope you find this article helpful and informative. If you have any further queries or recommendations, please feel free to comment here. And, visit ExcelDemy for many more articles like this.
