Going through my substitution section of my homework, and I successfully did most of them but had trouble with two of them:

Determine the intersection of the following systems:

a) y = 2x – 7 and y = - x^{2}-4 x – 3

Heres my attempt:

(2x-7)=-x^{2}-4x-3

0=x^{2 }-4x-3-2x+7

-1(0=-x^{2 }-6x+4)

0=x^{2}+6x-4

In every other question we've had we could just simplify this last step to end up with an answer like (x-x)(x-x), however with this one I can't see what multiplies to -4, and adds to 6

Then there's the second one

b) x^{2}+ y^{2}= 30 and 2 x – 3 y = 10

2x-3y=10 ~ y=2x+10

3 3

x^{2 }+(2x+10)^{2}= 30

.........3......3 [sorry about dots, still learning how to type in equations]

Is this correct so far? It doesn't feel like it is....