# 2×2 System of Equations Calculator

Enter a system of two **linear **equations to find its solution.

**Solution:**

Use this calculator to find the solution to a system of linear equations. Enter both equations and the solutions will be displayed at the bottom.

## How to use the systems of equations calculator?

**Step 1:** Enter the first equation in the first input box. You can use any variable as long as it is consistent with the second equation.

**Step 2:** Enter the second equation in the second input box. Use the same variables from the first equation.

**Step 3:** Click “Solve” to get the solution to the system of equations.

**Step 4:** The solution along with the linear system entered will be displayed at the bottom.

## What type of equations does the calculator support?

The calculator supports only systems of linear equations. That is, you can only enter equations that have the form 2x+2y=5. However, you can enter the equations regardless of the order of the terms. For example, 2y=-3x+2 as well as 3x+2y=2 are valid options.

## What is a 2×2 system of equations?

A 2×2 system of equations is a system of two equations with two variables. To find the solution to the 2×2 system of linear equations, the equations have to be solved simultaneously, and the solution has to satisfy both equations at the same time.

## What are the methods for solving 2×2 systems of equations?

To manually solve 2×2 systems of linear equations, there are three main methods: the substitution method, the elimination method, and the graphical method.

### Solve systems of equations by the substitution method

To solve systems of equations using the substitution method, we have to follow these steps:

- Simplify if possible. Remove parentheses or other grouping signs, combine like terms, and eliminate fractions.
- Solve one of the two equations for any variable.
- Substitute the expression obtained in step 2 into the other equation. This will give us an equation with only one variable.
- Solve for the remaining variable. Solve the resulting equation from Step 3 for the remaining variable.
- Substitute the value of the variable found to solve for the second variable.
- Check the solution in both equations.

### Solve systems of equations by the elimination method

To solve systems of equations using the elimination method we follow these steps:

- Simplify if possible and write the equations in the form Ax+By=C. Remove parentheses or other grouping signs, combine like terms, and eliminate fractions.
- Multiply one or both equations by a number that will create opposite coefficients for either variable. We are going to add the equations and we need one of the variables to be eliminated after the addition is done.
- Add the equations. By doing this, one of the variables will be eliminated and we will obtain one equation with only one variable.
- Solve for the remaining variable.
- Substitute the found value into either equation and solve for the second variable.
- Check the solution in both equations.

If you want to learn how to solve 2×2 systems of equations manually, you can take a look at our guide to solving systems of equations.

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