What is the value of y in the solution to the system of equations?One-thirdx + One-fourthy = 12x – 3y = –30A. –8B. –3C. 3D. 8

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]