Answer:
A.
Step-by-step explanation:
[tex]y=2x+4[/tex]
[tex]y=x^2+x-2[/tex]
Both equations are solved for y so I'm just going to substitute
the 1st y (the 2x+4) into the second equation's y.
[tex]2x+4=x^2+x-2[/tex]
I'm going to get everything on one side so I have 0=ax^2+bx+c.
Subtract 2x and subtract 4 on both sides:
[tex]0=x^2-x-6[/tex]
Since the coefficient of x^2 is 1, all we have to do is find two numbers that multiply to be -6 and add up to be -1.
These numbers are -3 and 2.
So the factored form of our equation is:
[tex]0=(x-3)(x+2)[/tex]
This means we have x-3=0 or x+2=0.
x-3=0
Add 3 on both sides:
x=3
x+2=0
Subtract 2 on both sides:
x=-2
So now we need to find y. I'm going to choose to use the easier equation:
y=2x+4.
If x=3, then y=2(3)+4=6+4=10. The ordered pair (3,10) is a solution.
If x=-2, then y=2(-2)+4=-4+4=0. The orded pair (-2,0) is a solution.
