Question

What are the solutions to the following system?

StartLayout Enlarged left-brace 1st row negative 2 x squared + y = negative 5 2nd row y = negative 3 x squared + 5 EndLayout
(0, 2)
(1, –2)
(StartRoot 2 EndRoot, negative 1) and (negative StartRoot 2 EndRoot, negative 1)
(StartRoot 5 EndRoot, negative 10) and (negative StartRoot 5 EndRoot, negative 10)

Answer 1

Substitute y = -3x^2 + 5 into -2x^2 + y = -5:

-2x^2 + (-3x^2 + 5) = -5
-5x^2 + 5 = -5
-5x^2 = -10
x^2 = 2 ⇒ x = ±√2.

Then y = -3(2) + 5 = -1.

Solutions: (√2, -1) and (−√2, -1).