Q14. Elimination

Question

6x + 6y = 150

6x + 5y = 90

Solve for x.

Explanation

There are a number of ways to solve this. We’ll work on elimination here.

6x + 6y = 180

6x + 5y = 120

0x + y = 60

y = 60

Plug y = 60 into either of the equations.

6x + 6(60) = 180

6x +360 = 180

6x = -180

x = -30

Lesson

You will almost certainly get a system of equation question on the exam.

If, in the equations, the constants next to the variables are the same (e.g. 6x and 6x), then you it makes sense to use elimination for this type of question. Often times you may need to adjust the equation(s) to get the constants to match. For example, one equation may have 3x and the other 6x. In that case, you’d have to multiply the full 3x equation by 2.

One more important item to note. Always pay attention to what the question is asking. Sometimes these types of questions will ask you to solve for the variable X, other times the variable Y, and other times it may be an expression like X + Y.

For students I tutor, I always have them underline what is being asked in every system of equation question.