Question

Find all solutions (x,y) of the given system, where x and y are real numbers.

xy=8
y=-x^2

Answer 1

Answer: (x, y) = (-2, -4)

Work Shown:

xy = 8

x(-x^2) = 8

-x^3 = 8

x^3 = -8

x = cube root of -8

x = -2

y = -x^2

y = -(-2)^2

y = -4

You can use a graphing tool like Desmos or GeoGebra to plot the two curves. Notice they intersect at (-2,-4) to confirm the answer. See the diagram below.