SOLUTION: how do u do substitution for systems of equations when one line is a quadratic

Question 971246: how do u do substitution for systems of equations when one line is a quadratic
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
same way as for two linear equations.
the substitution, however, should be done with the linear equation rather than the quadratic equation.

for example:

y = x + 1
y = x^2 + 2x + 1

replace y with x + 1 to get x + 1 = x^2 + 2x + 1
subtract x and subtract 1 from both sides of the equation to get:
x^2 + x = 0
factor out the x to get x * (x+1) = 0
solve for x to get x = 0 or x = -1

when x = 0, x + 1 = 1 and x^2 + 2x + 1 = 1
when x = -1, x + 1 = 0 and x^2 + 2x + 1 = 1 - 2 + 1 = 0

you have a common solution of x = 0 and x = -1.

solve for y or x in the linear equation and then use that value to substitute in the quadratic equation.

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