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

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) (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 (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=640 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 2.81916235697489, 0.873145335332806. Here's your graph:

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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.

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