Solve the system by the addition method.
-$$\left\{ \begin{array} { l }
6 x + 3 y = 51 \
2 x - 6 y = 38
\end{array} \right.$$
A) $\{ ( x , y ) \mid 2 x - 6 y = 38 \}$
B) $\{ ( - 3,10 ) \}$
C) $\{ ( 10 , - 3 ) \}$
D) $\varnothing$

Question

Solve the system by the addition method.
-$$\left\{ \begin{array} { l } 
6 x + 3 y = 51 \
2 x - 6 y = 38
\end{array} \right.$$
A) $\{ ( x , y ) \mid 2 x - 6 y = 38 \}$
B) $\{ ( - 3,10 ) \}$
C) $\{ ( 10 , - 3 ) \}$
D) $\varnothing$

Quizplus · Accepted Answer

To solve the system by the addition method, we first make the coefficients of one of the variables the same in both equations. Multiplying the second equation by 3 gives us $6x - 18y = 114$. Adding this to the first equation $6x + 3y = 51$ eliminates $x$, leading to $-15y = 63$, which simplifies to $y = -3$. Substituting $y = -3$ into one of the original equations to solve for $x$ gives $x = 10$. Therefore, the solution is $(10, -3)$.

Solve the System by the Addition Method {6x+3y=512x−6y=38\left\{ \begin{array} { l } 6 x + 3 y = 51 \\2 x - 6 y = 38\end{array} \right.{6x+3y=512x−6y=38​

Solve the System by the Addition Method $\left\{ \begin{array} { l } 6 x + 3 y = 51 \\2 x - 6 y = 38\end{array} \right.$