SOLUTION: Please help me solve this equation: y = 3x-3 Y = {{{y^2-2x}}}

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Question 800970: Please help me solve this equation:
y = 3x-3
Y = y%5E2-2x
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me solve this equation:
y = 3x-3
y = y%5E2-2x
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It's 2 equations.
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Sub for y in the 2nd equation
3x-3+=+%283x-3%29%5E2+-+2x
9x%5E2+-+20x+%2B+9+=+3x-3
9x%5E2+-+23x+%2B+12+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 9x%5E2%2B-23x%2B12+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-23%29%5E2-4%2A9%2A12=97.

Discriminant d=97 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--23%2B-sqrt%28+97+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-23%29%2Bsqrt%28+97+%29%29%2F2%5C9+=+1.82493654454423
x%5B2%5D+=+%28-%28-23%29-sqrt%28+97+%29%29%2F2%5C9+=+0.730619011011328

Quadratic expression 9x%5E2%2B-23x%2B12 can be factored:
9x%5E2%2B-23x%2B12+=+%28x-1.82493654454423%29%2A%28x-0.730619011011328%29
Again, the answer is: 1.82493654454423, 0.730619011011328. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B-23%2Ax%2B12+%29

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y = 3x - 3 for 2 values of x.