Solve the system by using the substitution method. $$\left( \begin{array} { l }
x = - 5 y \
2 x - 2 y = - 12
\end{array} \right)$$
A) (5, -1)
B) (1, -5)
C) (-5, 1)
D) infinitely many solutions
E) no solutions

Question

Solve the system by using the substitution method. $$\left( \begin{array} { l } 
x = - 5 y \
2 x - 2 y = - 12
\end{array} \right)$$
A) (5, -1)
B) (1, -5)
C) (-5, 1)
D) infinitely many solutions
E) no solutions

Quizplus · Accepted Answer

Using the first equation, we can substitute $-5y$ for $x$ in the second equation:
$$2(-5y) - 2y = -12$$
Simplifying this equation, we get $-12y=-12$, which means $y=1$. To find $x$, we can substitute $1$ for $y$ in the first equation:
$$x = -5(1)$$
Simplifying this equation, we get $x=-5$. Therefore, the solution to the system is $(x,y)=(-5,1)$, which corresponds to choice C.

Solve the System by Using the Substitution Method (x=−5y2x−2y=−12)\left( \begin{array} { l } x = - 5 y \\2 x - 2 y = - 12\end{array} \right)(x=−5y2x−2y=−12​)

Solve the System by Using the Substitution Method $\left( \begin{array} { l } x = - 5 y \\2 x - 2 y = - 12\end{array} \right)$