# Examples of elimination method in linear equations

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## What is elimination method in linear equations?

In the

**elimination method**you either add or subtract the**equations**to get an**equation**in one variable. When the coefficients of one variable are opposites you add the**equations**to**eliminate**a variable and when the coefficients of one variable are equal you subtract the**equations**to**eliminate**a variable.## How do you solve a question by elimination?

**Steps**

**for Solving**Equations through the**Elimination Method**- The first step is to multiply both the linear equations by a constant on non-zero value. This would make the coefficients of either of the variables, x or y, numerically equal.
- The next step is adding or subtracting one equation from the other in a way that one of the variables is easily eliminated.

## Why does elimination method work?

Because it enables us to eliminate or get rid of one of the variables, so we can solve a more simplified equation. Some textbooks refer to the

**elimination method**as the addition**method**or the**method**of linear combination. This is because we are going to combine two equations with addition!## Why does Gaussian elimination work?

We know that adding and subtracting equations does not change the solution set, so the first set of equations has the same solution as the second set. Thus the step in

**Gaussian elimination**is “valid”. And you keep doing such steps until you get the matrix in echelon form, which is easy to handle.