Question

Solve the following system of equations

-x^2+y^2=16
-2x^2+y^2=16
Provide your answer below
(x, y) (x, y)

Answer 1

The solutions are (0, 4) and (0, -4)

Explanation:

Solve this system using substitution:

Take the negative of the first equation and add the result to the second one:

-x^2 + y^2 = 16 becomes x^2 - y^2 = -16

Then:

x^2 - y^2 = -16

-2x^2 + y^2 = 16

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-x^2 = 0, so x must be 0.

By the first equation, if x = 0, -(0)^2 + y^2 = 16, or

y^2 = 16, or y = ±4

The solutions are (0, 4) and (0, -4)