Question

X^2 + y^2 = 13,

x^2 - y^2 = 5

Check all of the following that are solutions to the system shown.
A. (3,2)
B.(3,-2)
C.(-3,2)
D. (-3,-2)

Answer 1

A, B, C and D. are solutions.

Explanation:

x^2 + y^2 = 13

x^2 - y^2 = 5

Check which roots fit the original equations:

If x = 3, A gives

9 + y^2 = 13 giving y = +/- √4 = 2 or -2.

Now plug in x = 3 and y = 2 in the second equation:

9 - (2)^2 = 5

Therefore (3,2) is a solution of the 2 equations.

Following the same procedure for B, C and D:

B. Substituting x = 3 and x = -2 fits both equations so (3, -2) is a solution.

The same is true for C and D.