SOLUTION: Solve the following non-linear systems and graph in the cartesian plane. You can use either Elimination, Substitution and make sure to identify the solutions by Graphing Method. Sh

Algebra ->  Systems-of-equations -> SOLUTION: Solve the following non-linear systems and graph in the cartesian plane. You can use either Elimination, Substitution and make sure to identify the solutions by Graphing Method. Sh      Log On


   

Question 1199494: Solve the following non-linear systems and graph in the cartesian plane. You can use either Elimination, Substitution and make sure to identify the solutions by Graphing Method. Show your Complete Solution.
3x+2y=8
x^2+y^2=8
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
3x+2y=8
x^2+y^2=8
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3x+2y=8 ---> y = -(3/2)x + 4
y^2 = (9x^2/4) - 12x + 16
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x^2+y^2=8
Sub for y^2
x^2 + (9x^2/4) - 12x + 16 = 8
4x^2 + 9x^2 - 48x + 32 = 0
13x^2 - 48x + 32 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 13x%5E2%2B-48x%2B32+=+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=%28-48%29%5E2-4%2A13%2A32=640.

Discriminant d=640 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--48%2B-sqrt%28+640+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-48%29%2Bsqrt%28+640+%29%29%2F2%5C13+=+2.81916235697489
x%5B2%5D+=+%28-%28-48%29-sqrt%28+640+%29%29%2F2%5C13+=+0.873145335332806

Quadratic expression 13x%5E2%2B-48x%2B32 can be factored:
13x%5E2%2B-48x%2B32+=+%28x-2.81916235697489%29%2A%28x-0.873145335332806%29
Again, the answer is: 2.81916235697489, 0.873145335332806. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+13%2Ax%5E2%2B-48%2Ax%2B32+%29

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Sub for x in 3x+2y=8 and find y.
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For the graph, DL the FREE software at www.padowan.dk
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Use F6 to enter the given relationships.