Solve the system by elimination.
-$$\begin{array} { l }
5 x + 9 y = 81 \
3 x - 3 y = - 27
\end{array}$$
A) $\{ ( 0,10 ) \}$
B) $\{ ( 0,9 ) \}$
C) $\varnothing$
D) $\{ ( - 1,10 ) \}$

Question

Solve the system by elimination.
-$$\begin{array} { l } 
5 x + 9 y = 81 \
3 x - 3 y = - 27
\end{array}$$
A) $\{ ( 0,10 ) \}$
B) $\{ ( 0,9 ) \}$
C) $\varnothing$
D) $\{ ( - 1,10 ) \}$

Quizplus · Accepted Answer

To solve by elimination, first simplify the second equation by dividing by 3: $x - y = -9$. Multiply this equation by 9 to eliminate $y$: $9x - 9y = -81$. Add this to the first equation: $5x + 9y + 9x - 9y = 81 - 81$, resulting in $14x = 0$, so $x = 0$. Substitute $x = 0$ into $x - y = -9$ to find $y = 9$. Thus, the solution is $(0, 9)$.

Solve the System by Elimination 5x+9y=813x−3y=−27\begin{array} { l } 5 x + 9 y = 81 \\3 x - 3 y = - 27\end{array}5x+9y=813x−3y=−27​

Solve the System by Elimination $\begin{array} { l } 5 x + 9 y = 81 \\3 x - 3 y = - 27\end{array}$