SOLUTION: Find the exact solutions of the system of equations x^2+2y^2=18 and x=2y Thanks

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Question 43860: Find the exact solutions of the system of equations x^2+2y^2=18 and x=2y
Thanks
Answer by adamchapman(301) About Me  (Show Source):
You can put this solution on YOUR website!
you know that y=2x, so replace y in the longer equation with 2x:
Now x^2+2y^2=18
Becomes x^2+2(2x)^2=18
This can be simplified:
x^2 + 2(4x^2) = 18
x^2 + 8x^2 = 18
9x^2=18
Now divide both side by 9:
x^2=9
So x=3 or x=-3
Recalling that y=2x;
y=6 or y=-6
This can be written in the form of coordinates on a graph, like this:
"The solutions are (3,6) and (-3,-6)"
I hope this helps.
If you have any other problems please don't hesitate to contact me at adam.chapman@student.manchester.ac.uk