Solve the system by substitution.
-$$\begin{array} { r }
x + 2 y = - 16 \
2 x + 2 y = - 22
\end{array}$$
A) $\varnothing$
B) $\{ ( - 6 , - 5 ) \}$
C) $\{ ( - 5 , - 6 ) \}$
D) $\{ ( 6 , - 6 ) \}$

Question

Solve the system by substitution.
-$$\begin{array} { r } 
x + 2 y = - 16 \
2 x + 2 y = - 22
\end{array}$$
A) $\varnothing$
B) $\{ ( - 6 , - 5 ) \}$
C) $\{ ( - 5 , - 6 ) \}$
D) $\{ ( 6 , - 6 ) \}$

Quizplus · Accepted Answer

To solve the system by substitution, we first solve one of the equations for one variable in terms of the other. From the first equation, we can solve for $x$:$$x = -16 - 2y$$Then, we substitute this expression for $x$ in the second equation:$$2(-16 - 2y) + 2y = -22$$Simplifying:$$-32 - 4y + 2y = -22$$$$-4y + 2y = 10$$$$-2y = 10$$$$y = -5$$Substitute $y = -5$ back into the expression for $x$:$$x = -16 - 2(-5)$$$$x = -16 + 10$$$$x = -6$$Therefore, the solution is $(-6, -5)$, which corresponds to choice B.

Solve the System by Substitution x+2y=−162x+2y=−22\begin{array} { r } x + 2 y = - 16 \\2 x + 2 y = - 22\end{array}x+2y=−162x+2y=−22​

Solve the System by Substitution $\begin{array} { r } x + 2 y = - 16 \\2 x + 2 y = - 22\end{array}$