Answer:
D. 8
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}\dfrac{1}{3}x+\dfrac{1}{4}y=1\\\\2x-4y=-30\end{cases}[/tex]
Multiply the first equation by -6:
[tex]\implies -6 \cdot \dfrac{1}{3}x+-6 \cdot \dfrac{1}{4}y=-6 \cdot 1[/tex]
[tex]\implies -2x-\dfrac{3}{2}y=-6[/tex]
Add this to the second equation to eliminate x:
[tex]\begin{array}{rrcccl}&2x &- &3y& = &-30\\\phantom{\dfrac12}+ &(-2x& - &\frac{3}{2}y &= &\;\;-6)\\\cline{2-6} \phantom{\dfrac12}&0&-&\frac{9}{2}y&=&-36\\ \cline{2-6}\end{array}[/tex]
Solve the equation for y:
[tex]\implies -\dfrac{9}{2}y=-36[/tex]
[tex]\implies \dfrac{9}{2}y=36[/tex]
[tex]\implies 9y=72[/tex]
[tex]\implies y=\dfrac{72}{9}[/tex]
[tex]\implies y=8[/tex]
