Solve the system by substitution.
-$$\begin{aligned}
3 x + 7 y & = 2 \
9 y & = 30 + 2 x
\end{aligned}$$
A) $\left. \left\{ - \frac { 192 } { 41 } , \frac { 94 } { 41 } \right) \right\}$
B) $\left\{ \left( - \frac { 192 } { 41 } , - \frac { 360 } { 41 } \right) \right\}$
C) $\left\{ \left( - \frac { 192 } { 41 } , - \frac { 40 } { 41 } \right) \right\}$
D) $\left\{ \left( \frac { 94 } { 41 } , - \frac { 192 } { 41 } \right) \right\}$

Question

Quizplus · Accepted Answer

To solve the system by substitution, first solve one of the equations for one variable in terms of the other. From the second equation, $9y = 30 + 2x$, we can express $y$ in terms of $x$ as $y = \frac{30 + 2x}{9}$. Substituting this expression for $y$ in the first equation, $3x + 7(\frac{30 + 2x}{9}) = 2$, and solving for $x$ gives $x = -\frac{192}{41}$. Substituting $x = -\frac{192}{41}$ back into the expression for $y$, we find $y = \frac{94}{41}$. Therefore, the solution is $\left(-\frac{192}{41}, \frac{94}{41}\right)$.

Solve the System by Substitution 3x+7y=29y=30+2x\begin{aligned}3 x + 7 y & = 2 \\9 y & = 30 + 2 x\end{aligned}3x+7y9y​=2=30+2x​

Solve the System by Substitution $\begin{aligned}3 x + 7 y & = 2 \\9 y & = 30 + 2 x\end{aligned}$