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!

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- Nov 12th 2013, 08:13 PMStephenSkinnerSystem of Equations HELP
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! - Nov 12th 2013, 08:34 PMProve ItRe: System of Equations HELP
Write y in terms of x (from the second equation), substitute it into the first equation, then solve the quadratic.

- Nov 12th 2013, 08:50 PMStephenSkinnerRe: System of Equations HELP
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. - Nov 12th 2013, 08:53 PMStephenSkinnerRe: System of Equations HELP
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. - Nov 12th 2013, 09:08 PMSlipEternalRe: System of Equations HELP
$\displaystyle (2x+12)(x-8) = 2x^2+12x-16x-96 = 2x^2-4x-96$, so you have the signs backwards. It should be $\displaystyle 2(x-6)(x+8) = 0$ (note: I factored out the 2). Hence $\displaystyle x = 6, x = -8$. Now, plug those values in for $\displaystyle y = x+2$.

Finally, plug in both sets of values you found for $\displaystyle x$ and $\displaystyle y$ to the first equation to make sure it is correct. - Nov 12th 2013, 09:41 PMStephenSkinnerRe: System of Equations HELP