SOLUTION: Please help. I'm not sure if this is the right section. This is from a worksheet. Find the exact solutions of the system of equations x^2+2y^2=18 and x=2y I must show my work.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help. I'm not sure if this is the right section. This is from a worksheet. Find the exact solutions of the system of equations x^2+2y^2=18 and x=2y I must show my work.       Log On


   

Question 167187: Please help. I'm not sure if this is the right section. This is from a worksheet.
Find the exact solutions of the system of equations x^2+2y^2=18 and x=2y
I must show my work.
I'm completely lost.
Thanks
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.x%5E2%2B2y%5E2=18
2.x=2y
Substitute eq. 2 into eq. 1, directly substitute for x and solve for y.
Then go back and find x.
1.x%5E2%2B2y%5E2=18
%282y%29%5E2%2B2y%5E2=18
4y%5E2%2B2y%5E2=18
6y%5E2=18
y%5E2=3
y=0+%2B-+sqrt%283%29
Then from eq. 2,
2.x=2y
x=2%280+%2B-+sqrt%283%29%29
x=0+%2B-+2%2Asqrt%283%29
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When we graph the equations, you can see the solutions more clearly.
Equation 1 is the ellipse.
Equation 2 is the straight line.
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(1.73,3.46) and (-1.73,-3.46)
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