SOLUTION: What point is the intersection of the graphs of x^2

SOLUTION: What point is the intersection of the graphs of x^2 - y^2 = 5 and 2x^2 + y^2 = 22 ?

Question 623493: What point is the intersection of the graphs of x^2 - y^2 = 5 and 2x^2 + y^2 = 22 ?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
You can solve this graphically and you can solve it algebraically.
algebraicclly, you solve as follows:
your 2 equations are:
x^2 - y^2 = 5
2x^2 + y^2 = 22
add the 2 equations to get:
3x^2 = 27
divide both sitdes of this equation by 3 to get:
x^2 = 9
take the square root of both sides of this equation to get:
x = +/- 3
substitute for x in either equation to get:
y = +/- 2
example:
in first equation:
x^2 - y^2 = 5 becomes:
9 - y^2 = 5 which becomes:
y^2 = 4 which becomes:
y = +/- 2
do it in the second equation and you get the same answer.
x = +/- 3
y = +/- 2 are your answers.
graphically you would solve as follows:
solve for y in terms of x in both equations.
x^2 - y^2 = 5 becomes:
y = +/- sqrt(x^2-5)
2x^2 + y^2 = 22 becomes:
y = +/- sqrt(22-2x^2)
graph of both of these equations is shown below:

solution is at the intersection points of the circle and the ellipse.
those points are (-3,2), (-3,-2), (3,2), (3,-2)

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