Hi, I am really stuck with this equations. I am so lost and dont know what to do. Please help.

Hi, I am really stuck with this equations. I am so lost and dont know what to do. Please help.

\(\displaystyle \frac{x - 2}{3} + \frac{y - 1}{4} = \frac{13}{12} \)

(eq.1)
\(\displaystyle \frac{2 - x}{2} + \frac{3 + y}{3} = \frac{11}{6} \)

(eq.2)

I'll do \(\displaystyle \frac{x - 2}{3} + \frac{y - 1}{4} = \frac{13}{12} \) you try the other one.

First thing to do is get rid of denominators, so multiply everything by 3 to get: \(\displaystyle x - 2 + \frac{3(y - 1)}{4} = \frac{3(13)}{12} \)

Now multiply by 4: \(\displaystyle 4x - 4(2) + 3(y - 1) = \frac{4(39)}{12} \)

Simplify: \(\displaystyle 4x -8 + 3y - 3 = \frac{156}{12} \)

Thus: \(\displaystyle 4x+ 3y - 11 = \frac{156}{12} \)

Add 11 to both sides: \(\displaystyle 4x+ 3y = \frac{156}{12}+11 \)

Subtract 3y from both sides: \(\displaystyle 4x = \frac{156}{12}+\frac{12(11)}{12}-3y\)

Then divide by 4: \(\displaystyle x = \frac{156}{4(12)}+\frac{12(11)}{4(12)}-\frac{3y}{4}\)

Solve: \(\displaystyle x = \frac{156}{48}+\frac{132}{48}-\frac{12(3y)}{12(4)}=\frac{156+138}{48}-\frac{36y}{48}=\frac{294-36y}{48}\)

That can be simplified to: \(\displaystyle \boxed{x=\frac{49-6y}{8}}\)