Solve the system.
$$\begin{array} { l }
9 x + 9 y = 37 \
- 7 x + 11 y = 37
\end{array}$$
A) $\left( \frac { 37 } { 81 } , \frac { 296 } { 81 } \right)$
B) $\left( \frac { 37 } { 18 } , - \frac { 148 } { 9 } \right)$
C) $\left( \frac { 37 } { 18 } , - \frac { 2 } { 9 } \right)$
D) $\left( \frac { 37 } { 81 } , - \frac { 2 } { 9 } \right)$

Question

Solve the system.
$$\begin{array} { l } 
9 x + 9 y = 37 \
- 7 x + 11 y = 37
\end{array}$$
A) $\left( \frac { 37 } { 81 } , \frac { 296 } { 81 } \right)$
B) $\left( \frac { 37 } { 18 } , - \frac { 148 } { 9 } \right)$
C) $\left( \frac { 37 } { 18 } , - \frac { 2 } { 9 } \right)$
D) $\left( \frac { 37 } { 81 } , - \frac { 2 } { 9 } \right)$

Quizplus · Accepted Answer

To solve the system, we can use the method of elimination or substitution. Here, we'll use elimination for simplicity. First, we can multiply the first equation by 7 and the second equation by 9 to make the coefficients of $x$ in both equations equal but opposite in sign:$$63x + 63y = 259$$$$-63x + 99y = 333$$Adding these two equations eliminates $x$, giving us:$$162y = 592$$Solving for $y$, we get:$$y = \frac{592}{162} = \frac{296}{81}$$Substituting $y$ back into one of the original equations to solve for $x$, we use the first equation:$$9x + 9(\frac{296}{81}) = 37$$$$9x = 37 - 9(\frac{296}{81})$$$$9x = \frac{3333 - 2664}{81}$$$$9x = \frac{669}{81}$$$$x = \frac{669}{729} = \frac{37}{81}$$Therefore, the solution is $\left( \frac { 37 } { 81 } , \frac { 296 } { 81 } \right)$, which corresponds to choice A.

Solve the System 9x+9y=37−7x+11y=37\begin{array} { l } 9 x + 9 y = 37 \\- 7 x + 11 y = 37\end{array}9x+9y=37−7x+11y=37​

Solve the System $\begin{array} { l } 9 x + 9 y = 37 \\- 7 x + 11 y = 37\end{array}$