Question

Which system is equivalent to StartLayout Enlarged left-brace 1st row y = negative 2 x squared 2nd row y = x minus 2 EndLayout?
StartLayout Enlarged left-brace 1st row y = negative 2 y squared minus 2 2nd row x = y minus 2 EndLayout
StartLayout Enlarged left-brace 1st row y = negative 2 y squared + 2 2nd row x = y + 2 EndLayout
StartLayout Enlarged left-brace 1st row y = negative 2 y squared minus 8 y minus 8 2nd row x = y + 2 EndLayout
StartLayout Enlarged left-brace 1st row y = negative 2 y squared + 8 y minus 8 2nd row x = y minus 2 EndLayout

Answer 1

Substitute x = y + 2 (from y = x − 2) into y = −2x^2:

y = −2(y + 2)^2 = −2(y^2 + 4y + 4) = −2y^2 − 8y − 8.

So the equivalent system is
y = −2y^2 − 8y − 8
x = y + 2.