Question

How do I solve these linear system problems? I solved it many times but it never seems right.

1. x^2 + y^2 =9
2x - y = -6

2.x^2 - x -y =0
x - y = -3

3. 2x^2 - x - y = -1
3x + y = 5

Answer 1

In each of your problems the linear equation can be easily expressed in terms of y.
Then sub that into the other equation

I will do #2

from x-y = -3
y = x+3

subbing into the other:
x^2 - x - (x+3) = 0
x^2 - 2x - 3 = 0
(x-3)(x+1) = 0
x = 3 or x = -1

if x = 3, y = 3+3 = 6
if x = -1, y = -1+3 = 2

here is a picture of our problem:

http://www.wolframalpha.com/input/?i=plot+x%5E2+-+x+-y+%3D0+,+x+-+y+%3D+-3

try the other two in the same way