Answer:
3y - x = -6
4y - x = 44
Explanation:
The given equation is
[tex]\frac{1}{3}x-2=\frac{1}{4}x+11[/tex]
We can say that these expressions are equal because both are equal to y, so we have the following equations
[tex]\begin{gathered} y=\frac{1}{3}x-2 \\ \\ y=\frac{1}{4}x+11 \end{gathered}[/tex]
Now, we can rewrite the first equation as
[tex]\begin{gathered} y=\frac{1}{3}x-2 \\ \\ 3y=3(\frac{1}{3}x)-3(2) \\ \\ 3y=x-6 \\ 3y-x=x-6-x \\ 3y-x=-6 \end{gathered}[/tex]
In the same way, we can rewrite the second equation as
[tex]\begin{gathered} y=\frac{1}{4}x+11 \\ \\ 4y=4(\frac{1}{4}x)+4(11) \\ \\ 4y=x+44 \\ 4y-x=x+44-x \\ 4y-x=44 \end{gathered}[/tex]
Therefore, the system of equations is
3y - x = -6
4y - x = 44
