Solve Nonlinear Systems By Addition
-$x ^ { 3 } + y = 0$ $5 x ^ { 2 } - y = 0$
A) $\{ ( 0,0 ) , ( - 5,125 ) \}$
B) $\{ ( 0,0 ) , ( 5 , - 125 ) \}$
C) $\{ ( 0,0 ) , ( - 5,25 ) \}$
D) $\{ ( - 1,1 ) , ( - 5,125 ) \}$

Question

Quizplus · Accepted Answer

To solve the system, add the two equations: $x^3 + y + 5x^2 - y = 0$, simplifying to $x^3 + 5x^2 = 0$. Factoring out $x^2$, we get $x^2(x + 5) = 0$, which gives solutions $x = 0$ and $x = -5$. Substituting $x = 0$ into the second equation gives $y = 0$, and substituting $x = -5$ into the second equation gives $y = 125$. Therefore, the solutions are $(0,0)$ and $(-5, 125)$.

Solve Nonlinear Systems by Addition - x3+y=0x ^ { 3 } + y = 0x3+y=0

Solve Nonlinear Systems by Addition
- $x ^ { 3 } + y = 0$