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

To solve the system by substitution, first solve one of the equations for one variable in terms of the other. From the second equation, $x = 21 - y$. Substitute this expression for $x$ in the first equation: $\frac{1}{5}(21 - y) + \frac{1}{2}y = 8$. Solve for $y$, then substitute back to find $x$. The solution is $\left( \frac { 25 } { 3 } , \frac { 38 } { 3 } \right)$.

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 $\left\{ \begin{aligned}\frac { 1 } { 5 } x + \frac { 1 } { 2 } y & = 8 \\x + y & = 21\end{aligned} \right.$