Solve the system by the substitution method.
-$$\begin{array} { l }
y = 10 x - x ^ { 2 } \
2 x - y = - 15
\end{array}$$
A) $( 3,21 ) , ( 5,25 )$
B) $( 3,5 )$
C) $( - 3,9 ) , ( - 5,5 )$
D) $( 5,25 )$

Question

Solve the system by the substitution method.
-$$\begin{array} { l } 
y = 10 x - x ^ { 2 } \
2 x - y = - 15
\end{array}$$
A) $( 3,21 ) , ( 5,25 )$
B) $( 3,5 )$
C) $( - 3,9 ) , ( - 5,5 )$
D) $( 5,25 )$

Quizplus · Accepted Answer

Substitute $y = 10x - x^2$ into the second equation: $2x - (10x - x^2) = -15$. Simplify to get $x^2 - 8x + 15 = 0$. Factoring gives $(x-3)(x-5) = 0$, so $x = 3$ or $x = 5$. Substituting these values back into $y = 10x - x^2$ gives the pairs $(3, 21)$ and $(5, 25)$.

Solve the System by the Substitution Method y=10x−x22x−y=−15\begin{array} { l } y = 10 x - x ^ { 2 } \\2 x - y = - 15\end{array}y=10x−x22x−y=−15​

Solve the System by the Substitution Method $\begin{array} { l } y = 10 x - x ^ { 2 } \\2 x - y = - 15\end{array}$