Solve system of equations by the method of substitution.
$$\left\{ \begin{array} { r }
15 x ^ { 3 } - 25 y = 0 \
15 x - y = 0
\end{array} \right.$$
A) $( 0,0 ) , ( - 5 , - 75 ) , ( 5,75 )$
B) $( 0,0 ) , ( - 5,75 ) , ( 5,75 )$
C) $( 0,0 ) , ( 5 , - 75 ) , ( 5,75 )$
D) $( 0,0 ) , ( - 5,76 ) , ( 5,76 )$
E) $( 0,0 ) , ( - 5 , - 74 ) , ( 5,74 )$

Question

Solve system of equations by the method of substitution.
$$\left\{ \begin{array} { r } 
15 x ^ { 3 } - 25 y = 0 \
15 x - y = 0
\end{array} \right.$$
A) $( 0,0 ) , ( - 5 , - 75 ) , ( 5,75 )$
B) $( 0,0 ) , ( - 5,75 ) , ( 5,75 )$
C) $( 0,0 ) , ( 5 , - 75 ) , ( 5,75 )$
D) $( 0,0 ) , ( - 5,76 ) , ( 5,76 )$
E) $( 0,0 ) , ( - 5 , - 74 ) , ( 5,74 )$

Quizplus · Accepted Answer

From the second equation, $y = 15x$. Substituting $y$ in the first equation gives $15x^3 - 25(15x) = 0$, simplifying to $15x^3 - 375x = 0$, or $15x(x^2 - 25) = 0$, leading to $x = 0$, $x = 5$, and $x = -5$. Substituting these $x$ values back into $y = 15x$ gives the solutions $(0,0)$, $(5,75)$, and $(-5,-75)$.

Solve System of Equations by the Method of Substitution {15x3−25y=015x−y=0\left\{ \begin{array} { r } 15 x ^ { 3 } - 25 y = 0 \\15 x - y = 0\end{array} \right.{15x3−25y=015x−y=0​

Solve System of Equations by the Method of Substitution $\left\{ \begin{array} { r } 15 x ^ { 3 } - 25 y = 0 \\15 x - y = 0\end{array} \right.$