9514 1404 393
Answer:
(x, y) = (34/5, -4/5) = (6.8, -0.8)
Step-by-step explanation:
Subtract the first equation from the second to eliminate x.
[tex]\left(\dfrac{x}{3}-\dfrac{y}{2}\right)-\left(\dfrac{x-5}{3}+\dfrac{y+2}{3}\right)=\left(\dfrac{8}{3}\right)-(1)\\\\y\left(-\dfrac{1}{2}-\dfrac{1}{3}\right)+\left(\dfrac{5}{3}-\dfrac{2}{3}\right)=\dfrac{5}{3} \qquad\text{partially simplify}\\\\-\dfrac{5}{6}y=\dfrac{2}{3} \qquad\text{subtract 1}\\\\y=-\dfrac{4}{5} \qquad\text{multiply by $-\dfrac{6}{5}$}[/tex]
Substituting for y in the second equation, we can find x.
[tex]\dfrac{x}{3}-\dfrac{1}{2}\left(-\dfrac{4}{5}\right)=\dfrac{8}{3}\\\\5x +6=40 \qquad\text{multiply by 15}\\\\5x=34\qquad\text{subtract 6}\\\\x=\dfrac{34}{5}[/tex]
The solution is (x, y) = (34/5, -4/5) = (6.8, -0.8).
