Write y in terms of x (from the second equation), substitute it into the first equation, then solve the quadratic.
Solve the system:
x^2 + y^2 = 100
-x + y = 2
I don't know where to start because my teacher never taught us how to solve a system of equations where the variables are squared. If someone could show me how to do this then that'd be great. THANKS!
Okay. I got:
x^2 + y^2 = 100
-x + y = 2 ------> y = x + 2
x^2 + (x + 2)^2 = 100
x^2 + x^2 + 4x + 4 = 100
2x^2 + 4x = 96
2x^2 + 4x - 96 = 0
(2x + 12)(x - 8)
2x + 12 = 0
2x = -12
x = -6
x - 8 = 0
x = 8
So from here would I plug both x-values in to my 'y = x + 2' equation? Thus giving me 2 solutions to the system of equations? Idk if I'm doing this right.
Okay. I got:
x^2 + y^2 = 100
-x + y = 2 ------> y = x + 2
x^2 + (x + 2)^2 = 100
x^2 + x^2 + 4x + 4 = 100
2x^2 + 4x = 96
2x^2 + 4x - 96 = 0
(2x + 12)(x - 8)
2x + 12 = 0
2x = -12
x = -6
x - 8 = 0
x = 8
So from here would I plug both x-values in to my 'y = x + 2' equation? Thus giving me 2 solutions to the system of equations? Idk if I'm doing this right.