Answer:
y = 8 (Answer D.)
Step-by-step explanation:
We need to solve the following system of equations:
[tex]\frac{1}{3} x+\frac{1}{4} y=1\\2x-3y=-30[/tex]
so we start by multiplying both sides of the first equation by 12 so as to get rid of denominators and make our calculations simpler:
[tex]12\,(\frac{1}{3} x+\frac{1}{4} y)=12\,(1)\\4x+3y=12[/tex]
Since we are asked to solve for the unknown "y", we multiply the second equation of the system by "-2", because that way, the term in x will cancel out once we combine both equations term by term:
[tex](-2)\,(2x-3y)=(-2)\,(-30)\\-4x+6y=60[/tex]
now we combine the two modified equations to solve for the requested unknown "y":
[tex]4x+3y=12\\+\\-4x+6y=60\\---------\\0x+9y=72[/tex]
We can now easily solve for y:
[tex]0x+9y=72\\9y=72\\y=\frac{72}{9} \\y=8[/tex]
