SOLUTION: Solve the system of equations by substitution y = x^2 + 2x - 2 and y - 3x + 4

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Question 59973This question is from textbook Alegbra Concepts and Applications
: Solve the system of equations by substitution
y = x^2 + 2x - 2 and y - 3x + 4
This question is from textbook Alegbra Concepts and Applications

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the system of equations by substitution
y = x^2 + 2x - 2 and y - 3x + 4 <---you have a type-o here, I'm assuming that the - is supposed to be =.
y=x%5E2%2B2x-2 and y=3x%2B4
Se the two y's equal to each other:
x%5E2%2B2x-2=3x%2B4 Set = to 0
x%5E2%2B2x-3x-2-4=3x-3x%2B4-4
x%5E2-x-6=0 Factor
(x-3)(x+2)=0 Set each parenthesis = to 0.
x-3=0 and x+2=0
x-3+3=0+3 and x+2-2=0-2
x=3 and x=-2
Substitute 3 in for x in the linear equation because it's easiest.
y=3(3)+4
y=9+4
y=13 One solution is (3,13)
Sustitute -2 in for x in the same equation:
y=3(-2)+4
y=-6+4
y=-2 The second solution is (-2,-2)
Graphically, you can see the two points of intersection:
graph%28300%2C200%2C-10%2C10%2C-10%2C15%2Cx%5E2%2B2x-2%2C3x%2B4%29
Happy Calculating!!!