Answer:
x=34/5 , y= -4/5
Step-by-step explanation:
[tex]\begin{bmatrix}\frac{x-5}{3}+\frac{y+2}{3}=1\\ \frac{1}{3}x-\frac{1}{2}y=\frac{8}{3}\end{bmatrix}\\\\\\\frac{x-5}{3}+\frac{y+2}{3}=1\\\\\mathrm{Subtract\:}\frac{y+2}{3}\mathrm{\:from\:both\:sides}\\\\\frac{x-5}{3}+\frac{y+2}{3}-\frac{y+2}{3}=1-\frac{y+2}{3}\\\\Simplify\\\\\frac{x-5}{3}=1-\frac{y+2}{3}\\\\\mathrm{Multiply\:both\:sides\:by\:}3\\\\\frac{3\left(x-5\right)}{3}=3\times\:1-3\times\frac{y+2}{3}\\\\Simplify\\\\\frac{3\left(x-5\right)}{3} =x-5\\\\3\cdot \:1-3\cdot \frac{y+2}{3}[/tex]
[tex]=-y+1\\\\x-5=-y+1\\\\x-5=-y+1\\\\\mathrm{Add\:}5\mathrm{\:to\:both\:sides}\\\\x-5+5=-y+1+5\\\\Simplify\\\\x=-y+6\\\\\mathrm{Substitute\:}x=-y+6\\\\\begin{bmatrix}\frac{1}{3}\left(-y+6\right)-\frac{1}{2}y=\frac{8}{3}\end{bmatrix}\\\\Simplify\\\\\begin{bmatrix}\frac{-5y+12}{6}=\frac{8}{3}\end{bmatrix}\\\\Solve\:for\:y\\y=-\frac{4}{5}\\\\\mathrm{For\:}x=-y+6\\\\\mathrm{Substitute\:}y=-\frac{4}{5}\\\\x=\frac{34}{5}\\\\x=\frac{34}{5},\:y=-\frac{4}{5}[/tex]
