Solve the system algebraically.
-$$\begin{array} { l }
y = x ^ { 3 } - x ^ { 2 } \
y = 5 x ^ { 2 }
\end{array}$$
A) $( 0,0 )$ and $( 4,80 )$
B) $( 0,0 )$ and $( 6,180 )$
C) $( 0,0 )$ and $( 6,216 )$
D) $( 6,180 )$

Question

Solve the system algebraically.
-$$\begin{array} { l } 
y = x ^ { 3 } - x ^ { 2 } \
y = 5 x ^ { 2 }
\end{array}$$
A) $( 0,0 )$ and $( 4,80 )$
B) $( 0,0 )$ and $( 6,180 )$
C) $( 0,0 )$ and $( 6,216 )$
D) $( 6,180 )$

Quizplus · Accepted Answer

By setting the equations equal, $x^3 - x^2 = 5x^2$, simplifying gives $x^3 - 6x^2 = 0$. Factoring gives $x^2(x-6) = 0$, so $x = 0$ or $x = 6$. Substituting back, for $x = 0$, $y = 0$; for $x = 6$, $y = 180$. Thus, solutions are $(0,0)$ and $(6,180)$.

Solve the System Algebraically y=x3−x2y=5x2\begin{array} { l } y = x ^ { 3 } - x ^ { 2 } \\y = 5 x ^ { 2 }\end{array}y=x3−x2y=5x2​

Solve the System Algebraically $\begin{array} { l } y = x ^ { 3 } - x ^ { 2 } \\y = 5 x ^ { 2 }\end{array}$