+318 Use the elimination method to find all solutions of the system of equations. (Order your answers from smallest to largest x, then from smallest to largest y.)
2x^2 + 4y = 11
x^2-y^2=5/2
+129852 2x^2 + 4y = 11
x^2 -y^2 = 5/2
Multiply the second equation through by - 2 and we get that
2x^2 + 4y = 11
-2x^2 + 2y^2 = - 5 add these
2y^2 + 4y = 6
2y^2 + 4y - 6 = 0 divide through by 2
y^2 + 2y - 3 = 0 factor
(y + 3) ( y - 1) = 0
Setting each factor to 0 and solving for y we get that y = -3 and y = 1
And using 2x^2 + 4y = 11 we can find the values for x
2x^2 + 4(-3) = 11 2x^2 + 4(1) = 11
2x^2 - 12 = 11 2x^2 + 4 = 11
2x^2 = 23 2x^2 = 7
x^2 = 23/2 x^2 = 7/2
x = ±√[23/2] x = ±√[7/2]
So.....the solutions are
(x, y ) = (-3, ±√23/2] ) and ( 1 , ±√[7/2] )
