Question

what is the value of y in the solution to the system of equations?
\frac{1}{3}x + \frac{1}{4}y = 1
2x - 3y = -30
3
-3
8
-8

Explanation:

Step1: Simplify the first equation

Multiply the first equation \(\frac{1}{3}x+\frac{1}{4}y = 1\) by 12 to eliminate fractions:
\(12\times\frac{1}{3}x+12\times\frac{1}{4}y=12\times1\)
\(4x + 3y=12\).

Step2: Add the two equations

We now have the system:
\(

$$\begin{cases}4x + 3y=12\\2x-3y=-30\end{cases}$$

\)
Add the two equations to eliminate \(y\):
\((4x + 3y)+(2x-3y)=12+(-30)\)
\(6x=-18\)
Solve for \(x\): \(x=\frac{-18}{6}=-3\).

Step3: Substitute \(x\) to find \(y\)

Substitute \(x = -3\) into \(4x + 3y=12\):
\(4(-3)+3y=12\)
\(-12 + 3y=12\)
Add 12 to both sides: \(3y=24\)
Divide by 3: \(y = 8\).

Answer:

8 (corresponding to the third option, e.g., C. 8 if options are labeled A - D, but here the third box has 8)