System of Linear Equations: Elimination Method

System of Linear Equations: Elimination Method

How to solve system of linear equations problems by using the elimination method: example and its solutions. (2 ways)

Example

Solve the system of equations. x - y = 4, 2x + y = 5

Choose the variable to eliminate.
In this solution, let's choose y.

To eliminate y, add these two equations.
Then y will be eliminated.
And x = 3.

Put x = 3 into either of the equations.
Then y = -1.

So the answer is x = 3, y = -1.

Example: Another Solution

Solve the system of equations. x - y = 4, 2x + y = 5

Let's solve the same example
by choosing x to eliminate.

You can't eliminate x by directly adding.
So multiply 2 on both sides of the first equation.

And add these two equations.
Then x will be eliminated.
And y = -1.

Put y = -1 into either of the equations.
Then x = 3.

So the answer is x = 3, y = -1.

As you can see, you got the same answer.