Answer
$\left\{ \left( 7,3 \right) \right\}$ is the solution of the system of equations.
Work Step by Step
Step 1:
Solve for y in the second equation to obtain the value of y in terms of x:
Since, $y=\frac{5}{7}x-2$
Step 2:
Put $y=\frac{5}{7}x-2$ in the first equation to obtain the value of x:
$\begin{align}
& \frac{5}{7}x-2=\frac{1}{3}x+\frac{2}{3} \\
& \frac{5}{7}x-\frac{1}{3}x=2+\frac{2}{3} \\
& \frac{8}{21}x=\frac{8}{3} \\
& x=7
\end{align}$
Step 3:
Now, put the value, $x=7$ in the second equation to obtain the value of y:
$\begin{align}
& y=\frac{5}{7}\left( 7 \right)-2 \\
& =5-2 \\
& =3
\end{align}$
Thus, the solution set $\left( x,y \right)$ to the system of equation is $\left\{ \left( 7,3 \right) \right\}$.
