Solve the system by the addition method.
-$$\begin{array} { l }
- 6 x + y = 10 \
9 x + 4 y = - 4
\end{array}$$
A) $\left\{ \left( - \frac { 4 } { 3 } , 2 \right] \right\}$
B) $\{ ( 1 , - 6 ) \}$
C) $\left\{ \left( 4 , - \frac { 19 } { 4 } \right) \right\}$
D) $\left\{ \left( - \frac { 1 } { 3 } , 8 \right) \right\}$

Question

Solve the system by the addition method.
-$$\begin{array} { l } 
- 6 x + y = 10 \
9 x + 4 y = - 4
\end{array}$$
A) $\left\{ \left( - \frac { 4 } { 3 } , 2 \right] \right\}$
B) $\{ ( 1 , - 6 ) \}$
C) $\left\{ \left( 4 , - \frac { 19 } { 4 } \right) \right\}$
D) $\left\{ \left( - \frac { 1 } { 3 } , 8 \right) \right\}$

Quizplus · Accepted Answer

To solve the system by the addition method, we first make the coefficients of $y$ in both equations the same. Multiplying the first equation by 4 gives us $-24x + 4y = 40$. Now, adding this to the second equation $9x + 4y = -4$, we get $-15x = 36$, which simplifies to $x = -\frac{36}{15} = -\frac{12}{5} = -\frac{4}{3}$. Substituting $x = -\frac{4}{3}$ into the first equation, $-6(-\frac{4}{3}) + y = 10$, we find $y = 2$. Therefore, the solution is $\left\{ \left( - \frac { 4 } { 3 } , 2 \right) \right\}$.

Solve the System by the Addition Method −6x+y=109x+4y=−4\begin{array} { l } - 6 x + y = 10 \\9 x + 4 y = - 4\end{array}−6x+y=109x+4y=−4​

Solve the System by the Addition Method $\begin{array} { l } - 6 x + y = 10 \\9 x + 4 y = - 4\end{array}$