Question

What are the solutions to the system of equations?

{−x+y=4 y+12=x2+x
Responses

(−4,0) and (3,0)
begin ordered pair negative 4 comma 0 end ordered pair, and , begin ordered pair 3 comma 0 end ordered pair

(−4,0) and (4,8)
begin ordered pair negative 4 comma 0 end ordered pair, and , begin ordered pair 4 comma 8 end ordered pair

(0,4) and (4,8)
begin ordered pair 0 comma 4 end ordered pair, and , begin ordered pair 4 comma 8 end ordered pair

(−12,−12) and (3,0)

Answer 1

Answer: Option 2

Explanation:

`-x+y=4 \implies y=x+4\\\\y+12=x^2 +x \implies x+4+12=x^2 +x\\\\x+16=x^2 +x\\\\x^2 =16\\\\x=\pm 4\\\\x=-4 \implies y=-4+4=0\\\\x=4 \implies y=4+4=8\\\\\therefore (-4,0), (4,8)`