Solving Equations with

Linear Combinations

You are given two equations:

-5x + y = 1

9x - 2y = 4

The first thing you must do is isolate one of the variables to find its solution. You can start by getting rid of the y's in order to find the value of x. To do that you have to multiply all of equation one by 2

2(-5x + y = 1)

and get

-10x + 2y = 2

Then add equation two to the new equation one

-10x + 2y = 2

+9x - 2y =4

And get:

x = -6

Now that you have the value of x, all you have to do is substitute the x with -6.

-5(-6) + y = 1

Multiply the -5 and -6

30 + y = 1

Subtract the 30 from both sides and get the value of y:

y = -29

The solution of the equations is (-6, -29)