SOLUTION: 3rs-s^2=2 and 2r-3s=-4. Please solve and explain ,thanks

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Question 856323: 3rs-s^2=2 and 2r-3s=-4. Please solve and explain ,thanks
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
3rs-s^2=2
2r-3s=-4
.
2r=3s-4
r=(3s-4)/2
.
3s((3s-4)/2)-s^2=2
(9s^2-12s)/2-s^2=2
9s^2-12s-2s^2=4
7s^2-12s-4=0
s= -2/7, s=2 See below. I'll let you figure out r.
.
Ed
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 7x%5E2%2B-12x%2B-4+=+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=%28-12%29%5E2-4%2A7%2A-4=256.

Discriminant d=256 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--12%2B-sqrt%28+256+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-12%29%2Bsqrt%28+256+%29%29%2F2%5C7+=+2
x%5B2%5D+=+%28-%28-12%29-sqrt%28+256+%29%29%2F2%5C7+=+-0.285714285714286

Quadratic expression 7x%5E2%2B-12x%2B-4 can be factored:
7x%5E2%2B-12x%2B-4+=+7%28x-2%29%2A%28x--0.285714285714286%29
Again, the answer is: 2, -0.285714285714286. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+7%2Ax%5E2%2B-12%2Ax%2B-4+%29