Solving quadratic linear equations algebraically

Question 1

Example 1: x^2+y^2=100

x-y=2

Answer 1

1) Rearrange to make x or y the subject: x-y=2
x=2+y
2) Substitute into quadratic and solve:
x^2+y^2=100
(y+2)^2+y^2=100
(y+2)(y+2)=y^2+4y+4
y^2+4y+4+y^2=100
2y^2+4y-96=0
y^2+2y-48=0
-6 and 8 multiply and add to give 2 and -48
(y+8)(y-6)=0
y+8=0
[[[y=-8]]]
y-6=0
[[[y=6]]]
3) Find x
x=y+2
x=-8+2
[[[x=-6]]]
x=6+2
[[[x=8]]]
4)  Co-ordinates (-6,-8)
(8,6)

Question 2

Example 2: x^2+y^2=17

x+2y=2

Answer 2

x^2+y^2=17
x+2y=2
1) x=2-2y
(2-2y)^2+y^2=17
(2-2y)(2-2y)
4-4y-4y+4y^2
4-8y+4y^2+y^2=17
5y^2-8y-13=0
ac=-65
b=-8
5, -13
5y^2+5y-13y-13=0
First half: 5y^2+5y
5y(y+1)
Second half: -13y-13
-13(y+1)
(5y-13)(y+1)=0
As it doesn't ask for the x value or the y value we leave it like this I think