Solve the system by the addition method.
-$$\left\{ \begin{array} { l }
6 x + 27 y = 27 \
5 x - 9 y = - 9
\end{array} \right.$$
A) $\varnothing$
B) $\{ ( x , y ) \mid 5 x - 9 y = - 9 \}$
C) $\{ ( 0,1 ) \}$
D) $\{ ( 1,0 ) \}$

Question

Solve the system by the addition method.
-$$\left\{ \begin{array} { l } 
6 x + 27 y = 27 \
5 x - 9 y = - 9
\end{array} \right.$$
A) $\varnothing$
B) $\{ ( x , y ) \mid 5 x - 9 y = - 9 \}$
C) $\{ ( 0,1 ) \}$
D) $\{ ( 1,0 ) \}$

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:$$6x + 27y = 27$$$$15x - 27y = -27$$Adding these equations cancels out $y$, resulting in:$$21x = 0$$Solving for $x$ gives $x = 0$. Substituting $x = 0$ into one of the original equations to solve for $y$, we use the first equation:$$6(0) + 27y = 27$$$$27y = 27$$$$y = 1$$Therefore, the solution to the system is $(0, 1)$.

Solve the System by the Addition Method {6x+27y=275x−9y=−9\left\{ \begin{array} { l } 6 x + 27 y = 27 \\5 x - 9 y = - 9\end{array} \right.{6x+27y=275x−9y=−9​

Solve the System by the Addition Method $\left\{ \begin{array} { l } 6 x + 27 y = 27 \\5 x - 9 y = - 9\end{array} \right.$