Solve the following system of equations by substitution or elimination. Enter your answer as (x,y).

Question

x+3y = 6 -3x+2y = -18

Answer 1

Substitution works well also, as you can easily change x + 3y = 6 into x = 6 - 3y.

Then -3x + 2y = -18 becomes -3(6 - 3y) + 2y = -18. Use distributive rule to eliminate the parentheses.

-18 + 9y + 2y = -18 Combine like terms, etc.

11y = 0, so y = 0

x = 6 - 3(0) = 6

As usual, check by substituting the results into both original equations.

Answer 2

This is easiest solved by elimination which is the method I have found that most students prefer.

First multiply the first equation by 3 so it 'matches up' with the second equation for elimination of x.

3x + 9y = 18

-3x + 2y = -18

The x is now eliminated when we add the equations together and we get 11y = 0 therefore y = 0.

Now enter y = 0 into one of the original equations. You generally want to choose the one which looks easiest but it really doesn't matter. Choose the first equation and get x + 3(0) = 6 or x = 6.

Now check with the other equation.

-3(6) + 2(0) = -18

-18 = -18 check

So the solution is x = 6 and y = 0

As an ordered pair the solution is (6,0)