SOLUTION: Solve the system: x^2+y^2=100 y-x=2

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Question 606860: Solve the system:
x^2+y^2=100
y-x=2

Answer by sophxmai(62) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the system
x%5E2%2By%5E2=100
y-x=2

Solve the 2nd equation for y
y-x=2
y=x%2B2

So now you have
x%5E2%2By%5E2=100
y=x%2B2

Now substitute the 2nd equation into the 1st one
x%5E2%2B%28x%2B2%29%5E2=100

Now expand and group like terms
x%5E2%2B%28x%2B2%29%5E2=100
x%5E2%2Bx%5E2%2B4x%2B4=100
2x%5E2%2B4x-96=0

Now factor and solve
2x%5E2%2B4x-96=0
2%28x%5E2%2B2x-48%29=0
2%28x%2B8%29%28x-6%29=0

x%2B8=0 x-6=0
x=-8    x=6