Answer:
x = 3 and y = 8 → (3, 8)
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}3y+10x-54=0&\text{add 54 to both sides}\\5y-2x-34=0&\text{add 34 to both sides}\end{array}\right\\\left\{\begin{array}{ccc}3y+10x=54\\5y-2x=34&\text{multiply both sides by 5}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}3y+10x=54\\25y-10x=170\end{array}\right}\ \ \ \ |\text{add both sides of the equations}\\.\ \ \ \ \ 28y=224\qquad\text{divide both sides by 28}\\.\ \ \ \ \ \ \ \dfrac{28y}{28}=\dfrac{224}{28}\\.\ \ \ \ \ \ \ \boxed{y=8}[/tex]
[tex]\text{put the value of y to the first equation}\\\\3(8)+10x=54\\24+10x=54\qquad\text{subtract 24 from both sides}\\24-24+10x=54-24\\10x=30\qquad\text{divide both sides by 10}\\\dfrac{10x}{10}=\dfrac{30}{10}\\\boxed{x=3}[/tex]
