SOLUTION: 3x-4y=25 X^2-y^2=25

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Question 815416: 3x-4y=25
X^2-y^2=25
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
3x-4y=25
X^2-y^2=25
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3x-4y=25
y = (3x-25)/4
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X^2-y^2=25
x%5E2+-+%28%283x-25%29%2F4%29%5E2=25
16x%5E2+-+9x%5E2+%2B+150x+-+625+=+400
7x%5E2+%2B+150x+-+1025+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 7x%5E2%2B150x%2B-1025+=+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=%28150%29%5E2-4%2A7%2A-1025=51200.

Discriminant d=51200 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-150%2B-sqrt%28+51200+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28150%29%2Bsqrt%28+51200+%29%29%2F2%5C7+=+5.44815499854966
x%5B2%5D+=+%28-%28150%29-sqrt%28+51200+%29%29%2F2%5C7+=+-26.8767264271211

Quadratic expression 7x%5E2%2B150x%2B-1025 can be factored:
7x%5E2%2B150x%2B-1025+=+%28x-5.44815499854966%29%2A%28x--26.8767264271211%29
Again, the answer is: 5.44815499854966, -26.8767264271211. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+7%2Ax%5E2%2B150%2Ax%2B-1025+%29

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x+=+-75%2F7+%2B+80%2Asqrt%282%29%2F7
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x+=+-75%2F7+-+80%2Asqrt%282%29%2F7
Sub for x in the linear eqn and find y.