Solve the system of equations by using the substitution method.
-$$\begin{array} { l }
y = x ^ { 3 } \
y = 25 x
\end{array}$$
A) $\{ ( 0,0 ) , ( 5,125 ) \}$
B) $\{ ( 0,0 ) , ( 5,125 ) , ( - 5 , - 125 ) \}$
C) { }
D) $\{ ( 0,0 ) \}$

Question

Solve the system of equations by using the substitution method.
-$$\begin{array} { l } 
y = x ^ { 3 } \
y = 25 x
\end{array}$$
A) $\{ ( 0,0 ) , ( 5,125 ) \}$
B) $\{ ( 0,0 ) , ( 5,125 ) , ( - 5 , - 125 ) \}$
C) {  }
D) $\{ ( 0,0 ) \}$

Quizplus · Accepted Answer

Since both equations are equal to $y$, we can set them equal to each other: $x^3 = 25x$. This simplifies to $x^3 - 25x = 0$, or $x(x^2 - 25) = 0$, which factors further into $x(x - 5)(x + 5) = 0$. The solutions to this equation are $x = 0$, $x = 5$, and $x = -5$. Substituting these values back into either original equation to solve for $y$ gives the pairs $(0,0)$, $(5,125)$, and $(-5,-125)$.

Solve the System of Equations by Using the Substitution Method y=x3y=25x\begin{array} { l } y = x ^ { 3 } \\y = 25 x\end{array}y=x3y=25x​

Solve the System of Equations by Using the Substitution Method $\begin{array} { l } y = x ^ { 3 } \\y = 25 x\end{array}$