type the correct answer in each box. if necessary, use / for the fraction bar(s).\nfind the solution for…

Answer:

$x=\frac{5}{6}$, $y=\frac{8}{5}$

Explanation:

Step1: Eliminate $x$

Multiply the second equation $-6x + 5y=3$ by $2$: $$ \begin{align*} 2\times(-6x + 5y)&=2\times3\ -12x+10y&=6 \end{align*} $$ Add it to the first equation $12x + 15y=34$: $$ \begin{align*} (12x + 15y)+(-12x + 10y)&=34 + 6\ 12x+15y-12x + 10y&=40\ 25y&=40\ y&=\frac{40}{25}=\frac{8}{5} \end{align*} $$

Step2: Solve for $x$

Substitute $y = \frac{8}{5}$ into the second equation $-6x+5y = 3$: $$ \begin{align*} -6x+5\times\frac{8}{5}&=3\ -6x + 8&=3\ -6x&=3 - 8\ -6x&=-5\ x&=\frac{-5}{-6}=\frac{5}{6} \end{align*} $$