Solve the system by elimination.
-$$\begin{array} { l }
- 7 x - 6 y = - 13 \
- 3 x + 3 y = - 39
\end{array}$$
A) $\varnothing$
B) $\{ ( 7 , - 6 ) \}$
C) $\{ ( 6 , - 5 ) \}$
D) $\{ ( 7 , - 5 ) \}$

Question

Solve the system by elimination.
-$$\begin{array} { l } 
- 7 x - 6 y = - 13 \
- 3 x + 3 y = - 39
\end{array}$$
A) $\varnothing$
B) $\{ ( 7 , - 6 ) \}$
C) $\{ ( 6 , - 5 ) \}$
D) $\{ ( 7 , - 5 ) \}$

Quizplus · Accepted Answer

To solve the system by elimination, we can multiply the second equation by 2 to make the coefficients of $y$ opposites, which gives us $-6x + 6y = -78$. Adding this to the first equation $-7x - 6y = -13$ eliminates $y$, resulting in $-13x = -91$, so $x = 7$. Substituting $x = 7$ into one of the original equations, for example, the first one, gives $-7(7) - 6y = -13$, which simplifies to $-49 - 6y = -13$, leading to $-6y = 36$, so $y = -6$. Thus, the solution is $(7, -6)$.

Solve the System by Elimination −7x−6y=−13−3x+3y=−39\begin{array} { l } - 7 x - 6 y = - 13 \\- 3 x + 3 y = - 39\end{array}−7x−6y=−13−3x+3y=−39​

Solve the System by Elimination $\begin{array} { l } - 7 x - 6 y = - 13 \\- 3 x + 3 y = - 39\end{array}$