Question

(08.05)

A student is trying to solve the system of two equations given below:

Equation P: x + y = 8
Equation Q: 2x + 5y = 24

Which of the following steps can be used to eliminate the x term?
2(x + y = 8)
−2(x + y = 8)
−1(2x + 5y = 24)
−2(2x + 5y = 24)

Answer 1

If you use the first answer, the equation becomes 2x + 2y = 16. You could subtract this from equation Q to eliminate x.

The second answer makes equation P -2x - 2y = -16. You could add this to equation Q to eliminate x. You can use both of these methods to eliminate the x term, but if you can only choose one, you should choose the second option.

Answer 2

answer is −2(x + y = 8)
cause

−2(x + y = 8) (multiply -2 to 1st equation)
-2x - 2y = - 16
2x + 5y = 24
--------------------add
0 + 3y = 8 (eliminate x to solve for y)