Precalculus (6th Edition) Blitzer

$\left\{ \left( 7,3 \right) \right\}$ is the solution of the system of equations.
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 $\left\{ \left( 7,3 \right) \right\}$.