Solve Linear Systems by Addition
-$$\begin{array} { c }
x - 6 y = - 35 \
- 4 x - 7 y = - 15
\end{array}$$
A) $\{ ( - 5,5 ) \}$
B) $\{ ( - 6,6 ) \}$
C) $\{ ( 5,6 ) \}$
D) $\varnothing$

Question

Solve Linear Systems by Addition
-$$\begin{array} { c } 
x - 6 y = - 35 \
- 4 x - 7 y = - 15
\end{array}$$
A) $\{ ( - 5,5 ) \}$
B) $\{ ( - 6,6 ) \}$
C) $\{ ( 5,6 ) \}$
D) $\varnothing$

Quizplus · Accepted Answer

To solve the system of equations by addition, we first aim to eliminate one of the variables by adding the equations together. To eliminate $x$, we can multiply the first equation by 4 to get $4x - 24y = -140$. Adding this to the second equation $(-4x - 7y = -15)$ gives $-31y = -155$, which simplifies to $y = 5$. Substituting $y = 5$ into the first equation $x - 6(5) = -35$ gives $x = -5$. Therefore, the solution is $(-5, 5)$.

Solve Linear Systems by Addition - x−6y=−35−4x−7y=−15\begin{array} { c } x - 6 y = - 35 \\- 4 x - 7 y = - 15\end{array}x−6y=−35−4x−7y=−15​

Solve Linear Systems by Addition
- $\begin{array} { c } x - 6 y = - 35 \\- 4 x - 7 y = - 15\end{array}$