Question

Last question, I promise.
What is the solution of the linear quadratic system of equations?
y = x^2 + 5x - 3
y - x = 2

I need to be walked through it, not just given the answer. Will give fan and medal. Thank you in advance! :)

Answer 1

Do you plug the 2 in like this?
y = 2^2 + 5(2) - 3

Answer 2

Not exactly... check this out:

So you have
$$
y-x=2\\
y=2+x\\
$$
Plug in to your quadratic
$$
y=x^2+5x-3=2+x\\
x^2+5x-x-3-2=0\\
x^2+4x-5=0\\
(x-1)(x+5)=0
$$
So there are two solutions
if x=1 the equation is true
if x=-5 the equation is true

We know that y=2+x

So when x=1, y =3 and when x=-5, y = -3

Two solutions:
$$
(1,3)\text{ and }(-5,-3)
$$

Make sense?

Answer 3

Sorta. I'll have to look at it some more, but I get part of it. Thank you. :)