Answer:
[tex]\large\boxed{x=-\dfrac{1}{2},\ y=\dfrac{3}{2}}[/tex]
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}3x+5y=6&\text{multiply both sides by 4}\\-4x+2y=5&\text{multiply both sides by 3}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}12x+20y=24\\-12x+6y=15\end{array}\right}\qquad\text{add the both sides of the equations}\\.\qquad\qquad26y=39\qquad\text{divide both sides by 26}\\.\qquad\qquad y=\dfrac{39}{26}\\.\qquad\qquad y=\dfrac{39:13}{26:13}\\.\qquad\qquad\boxed{y=\dfrac{3}{2}}\\\\\text{Put the value of y to the second equation}[/tex]
[tex]-4x+2\left(\dfrac{3}{2}\right)=5\\-4x+3=5\qquad\text{subtract 3 from both sides}\\-4x=2\qquad\text{divide both sides by (-4)}\\x=\dfrac{2}{-4}\\x=-\dfrac{2:2}{4:2}\\\boxed{x=-\dfrac{1}{2}}[/tex]
