SOLUTION: solve systems of equations algebraically: y=2x^2-4x-5 and 3x-y=1

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Question 548001: solve systems of equations algebraically: y=2x^2-4x-5 and 3x-y=1
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
the equations represent a parabola and a straight line, looking like this: graph%28300%2C300%2C-3%2C7%2C-9%2C21%2C2x%5E2-4x-5%2C3x%2B1%29
3x-y=1 ---> y=3x-1
Substituting that expression in the other equation, we get
2x%5E2-4x-5=3x-1 --> 2x%5E2-7x-4=0
Then, applying the quadratic formula, we find

So the answers are x=-1%2F2 and x=4
Substituting into y=3x-1, we find
for x=-1%2F2 --> y=3%2A%28-1%2F2%29-1=-3%2F2-2%2F2=-5%2F2
for x=4 --> y=3%2A4-1=12-1=11
So the answers are points (-1/2,-5/2) and (4,11).