Question

What is the solution to the system of equations below?

y = 1/2x - 4 and y = -2x - 9

1. (-2, -5)
2. (-2, -3)
3. (2, -3)
4. (2, -13)

Answer 1

1. (-2, -5)

Explanation:

`\left\{\begin{array}{ccc}y=(1)/(2)x-4&(1)\\y=-2x-9&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\(1)/(2)x-4=-2x-9\qquad\text{multiply both sides by 2}\\\\x-8=-4x-18\qquad\text{add 8 to both sides}\\\\x=-4x-10\qquad\text{add 4x to both sides}\\\\5x=-10\qquad\text{divide both sides by 5}\\\\x=-2\\\\\text{put it to (2):}\\\\y=-2(-2)-9\\\\y=4-9\\\\y=-5`

Answer 2

4(y= 1/2x -4)

4y = 2x -16
y= -2x -9

5y = -25

Y= -5

So since there is only one answer with y= -5 the answer is A

Hope this helps!