Chapter 10 - Section 10.8 - Systems of Nonlinear Equations - 10.8 Exercises - Page 754: 7

{$-25,5$} and {$-25,-5$}

Given: $x+y^2=0$ and $2x+5y^2=75$ This implies that $x+y^2 \implies x=-y^2$ Then, we have $2(-y^2)+5y^2=75$ or, $3y^2=75 \implies y=\sqrt {25}$ This gives: $y=\pm 5$ a) At $y= 5$, we have $x=-(5)^2 \implies x=-25$ b) At $y=-5$, we have $x=-(-5)^2 \implies x=-25$ Thus, the solutions set are: {$-25,5$} and {$-25,-5$}