Solving 2-Variable Equations using Elimination

We solve 2-variable systems of equations using elimination whenever both x and y are on the same side of the equals sign for both equations. The idea of "elimination" is that we eliminate, or cross out one of the variables so that we can solve for one of them. Then, once you have one variable, plug it back in and solve for the other one. Express your answer as a coordinate pair.

Example: Solve the system of equations.

3x + 4y = 2
-3x - y = 7        -Cross out your x's first because 3x cancels out with -3x. Add the remaining terms.
       3y = 9       -Solve for y
         y = 3

Now, plug y = 3 into either of the equations and solve for x.
3x + 4(3) = 2
3x + 12 = 2    -Multiply
3x = -10         -Subtract 12 on both sides
x = -3.33        - Divide by 3 on both sides

Answer: (-3.33, 3) Express it as a coordinate pair.