Solving Systems: Elimination

System equations can be solved by:

• Graphing
• Substitution
• Elimination

Using Elimination to solve an equation can be done by lining up the two equations.

Next we observe them and see if we can easily eliminate x or y values by using a multiple.

For example, look at the following linear equations, how could we eliminate an x or y value if we were to add them together?

4y  + x = -17
-2y + 2x= 16

There are two ways we could eliminate a y or x value.

1. We could multiply x by -2, in the first equation, so it becomes -2
2. We could also multiply y in the 2nd equation by 2, so it becomes -4y

In either case it would eliminate one unknown, allowing us to solve for what remains:

4y  + x = -17
-2y + 2x= 16

-8y + -2x = 34
-2y +  2x = 16
--------------
-10y      = 50
y = -5

Now that y is discovered, we can plug the value in to get x. We can plug y into either of the original equations and see the value for x, like so:

4(-5) + x = -17
x - 20 = - 17
  + 20 = + 20
x      = 3

The answer is (3, -5)