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# Linear Combination Calculator

A linear equation is defined as an equation that is written for two different variables. This equation will be a linear combination of these two variables and a constant.

## What is a Linear Combination Calculator?

'**Linear Combination Calculator**' is an online tool that helps to calculate the variables for the given linear equations. Online Linear Combination Calculator helps you to calculate the variables for the given linear equations in a few seconds.

### Linear Combination Calculator

**NOTE:** Enter the coefficients upto two digits only.

## How to Use Linear Combination Calculator?

Please follow the steps below on how to use the calculator:

**Step 1:**Enter the coefficients of equations in the given input box.**Step 2:**Click on the**"Solve"**button to find the variables for the given linear equations.**Step 3:**Click on the**"Reset"**button to clear the fields and enter the new values.

## How to Find Linear Combination?

A linear equation of the form Ax + By = C. Here, x and y are variables, and A, B, and C are constants. A Linear combination calculator is used to solve a system of equations using the linear combination method also known as the elimination method.

To solve the variables of the given equations, let's see an example to understand briefly.

**Solved Examples on Linear Combination Calculator**

**Example 1:**

Solve the given linear combination equations 2x + y = 7 and x + y = 5 and verify it using linear combination calculator.

**Solution:**

2x + y = 7 ------> (1)

x + y = 5 -------> (2)

To eliminate 'y', subtract (1) - (2),

2x + y - x - y = 7 - 5

x = 2

Substitute x = 2 in equation(1),

2(2) + y = 7

4 + y = 7

y = 3

Therefore, x = 2, y = 3

**Example 2:**

Solve the given linear combination equations 3x - y = 4 and 4x - y = 7 and verify it using linear combination calculator.

**Solution:**

3x - y = 4 ------> (1)

4x - y = 7 -------> (2)

To eliminate'y', subtract (1) - (2),

3x - y - 4x + y = 4 - 7

-x = -3

x = 3

Substitute x = 3 in equation(1),

3(3) - y = 4

9 - y = 4

y = 5

Therefore, x = 3, y = 5

Similarly, you can try the linear combination calculator to solve the linear combination equations for:

- 7x + 8y = 17 and x - 16y = 4
- 11x - 17y = -18 and 12x - 15y = 8

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