SOLUTION: solve the following system of equations y=x^2-2x-2 y=x-4

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Question 41632: solve the following system of equations

y=x^2-2x-2
y=x-4
Answer by cstahl1(1) About Me  (Show Source):
You can put this solution on YOUR website!
if y=x-4 and y=x^2-2x-2 then x^2-2x-2=x-4;
add 4 to both sides: x^2-2x+2=x
subtract x from both sides: x^2-3x+2=0
factor x^2-3x+2: (x-2)(x-1)=0
one of these must equal 0: x-2=0 or x-1=0
x=2 or x=1
subsitute for both equations y=(2)-4=-2
y=(2)^2-2(2)-2=-2
so x=2 works
then see if x=1 works
subsitute: y=(1)-4=-3
y=(1)^2-2(1)-2=-3
so x=1 also works therefore x=2 and x=1