Question

Tao uses elimination to solve the following system of linear equations. -2x+4y=162x+2y=8Which ordered pair is a solution to the system?
a. (0, 4)
b. (0, 8)
c. (4, 0)
d. (8, 0)

Answer 1

The correct answer is the first option.

If you want to use elimination, you can sum the two equations for example, so that the x's simplify:

$(-2x+4y)+(2x+2y) = 16+8$

$6y = 24$

$y = 4$

Plug this value for y in one of the equations to derive the value of x:

$2x+2y=8 \implies 2x + 8 = 8 \implies x = 0$

So, the solution is $(x,y) = (0,4)$