Solve the system of equations below by the method of substitution. $\left\{ \begin{array} { l }
\frac { 3 } { 5 } x - \frac { 3 } { 2 } y = - \frac { 21 } { 10 } \
\
\frac { 5 } { 2 } x + \frac { 2 } { 7 } y = \frac { 335 } { 14 }
\end{array} \right.$
A) (9,5)
B) (7,3)
C) (5,5)
D) (3,7)
E) (1,1)

Question

Solve the system of equations below by the method of substitution. $\left\{ \begin{array} { l } 
\frac { 3 } { 5 } x - \frac { 3 } { 2 } y = - \frac { 21 } { 10 } \
\
\frac { 5 } { 2 } x + \frac { 2 } { 7 } y = \frac { 335 } { 14 }
\end{array} \right.$
A) (9,5)
B) (7,3)
C) (5,5)
D) (3,7)
E) (1,1)

Quizplus · Accepted Answer

Explanation:Solve the first equation for x.$\frac { 3 } { 5 } x - \frac { 3 } { 2 } y = - \frac { 21 } { 10 } $$\frac { 3 } { 5 } x = \frac { 3 } { 2 } y - \frac { 21 } { 10 } $$x = \frac { 5 } { 3 } \left( \frac { 3 } { 2 } y - \frac { 21 } { 10 } \right) $$x = \frac { 5 } { 2 } y - \frac { 35 } { 6 } $Substitute this expression for x into the second equation.$\frac { 5 } { 2 } x + \frac { 2 } { 7 } y = \frac { 335 } { 14 } $$\frac { 5 } { 2 } \left( \frac { 5 } { 2 } y - \frac { 35 } { 6 } \right) + \frac { 2 } { 7 } y = \frac { 335 } { 14 } $$\frac { 25 } { 4 } y - \frac { 175 } { 12 } + \frac { 2 } { 7 } y = \frac { 335 } { 14 } $$\frac { 175 } { 12 } y = \frac { 670 } { 14 } + \frac { 175 } { 12 } $$\frac { 175 } { 12 } y = \frac { 1275 } { 28 } $$y = \frac { 1275 } { 28 } \cdot \frac { 12 } { 175 } $$y = 5 $Substitute this value of y back into the first equation to solve for x.$\frac { 3 } { 5 } x - \frac { 3 } { 2 } y = - \frac { 21 } { 10 } $$\frac { 3 } { 5 } x - \frac { 3 } { 2 } (5) = - \frac { 21 } { 10 } $$\frac { 3 } { 5 } x - \frac { 15 } { 2 } = - \frac { 21 } { 10 } $$\frac { 3 } { 5 } x = - \frac { 21 } { 10 } + \frac { 15 } { 2 } $$\frac { 3 } { 5 } x = \frac { 9 } { 5 } $$x = \frac { 9 } { 5 } \cdot \frac { 5 } { 3 } $$x = 3 $Therefore, the solution to the system of equations is (3, 5).

Solve the System of Equations Below by the Method of Substitution