Solve the system by the method of substitution. $\left\{ \begin{aligned}
\frac { 1 } { 5 } x + \frac { 1 } { 2 } y & = 8 \
x + y & = 21
\end{aligned} \right.$
A) $\left( \frac { 25 } { 3 } , - \frac { 38 } { 3 } \right)$
B)(25,38)
C) $\left( - \frac { 25 } { 3 } , \frac { 38 } { 3 } \right)$
D) $\left( \frac { 25 } { 3 } , \frac { 38 } { 3 } \right)$
E)(-25,-38)

Question

Solve the system by the method of substitution.​ $\left\{ \begin{aligned}
\frac { 1 } { 5 } x + \frac { 1 } { 2 } y & = 8 \
x + y & = 21
\end{aligned} \right.$ ​
A) $\left( \frac { 25 } { 3 } , - \frac { 38 } { 3 } \right)$
B)(25,38)
C) $\left( - \frac { 25 } { 3 } , \frac { 38 } { 3 } \right)$
D) $\left( \frac { 25 } { 3 } , \frac { 38 } { 3 } \right)$
E)(-25,-38)

Quizplus · Accepted Answer

From the second equation, $x = 21 - y$. Substituting $x$ in the first equation gives $\frac{1}{5}(21 - y) + \frac{1}{2}y = 8$. Solving for $y$ yields $y = \frac{38}{3}$, and substituting $y$ back into $x = 21 - y$ gives $x = \frac{25}{3}$.

Solve the System by the Method of Substitution {15x+12y=8x+y=21\left\{ \begin{aligned}\frac { 1 } { 5 } x + \frac { 1 } { 2 } y & = 8 \\x + y & = 21\end{aligned} \right.⎩⎨⎧​51​x+21​yx+y​=8=21​

Solve the System by the Method of Substitution $\left\{ \begin{aligned}\frac { 1 } { 5 } x + \frac { 1 } { 2 } y & = 8 \\x + y & = 21\end{aligned} \right.$