<s>[INST] How to solve $\frac{11x+3y}{3x-1}+\frac{5x+2}{3}=9-\frac{3-y}{x-1}=12$ (multiple equality signs) How to answer an equation with multiple equality signs?
This is the equation:
$$\frac{11x+3y}{3x-1}+\frac{5x+2}{3}=9-\frac{3-y}{x-1}=12$$
I believe it can also be written in this format:
\begin{align}
\frac{11x+3y}{3x-1}+\frac{5x+2}{3}&=9-\frac{3-y}{x-1} \\ \\
\frac{11x+3y}{3x-1}+\frac{5x+2}{3}&= 12\\ 
9-\frac{3-y}{x-1} &= 12
\end{align}
How can this be solved?
 [/INST] Hint:
$$9-12=\frac{3-y}{x-1}$$
$$-3(x-1)=3-y$$
$$y=3x$$
Substitute this into
$$\frac{11x+3y}{3x-1}+\frac{5x+2}{3}=12$$
Solve for $x$, this is just a quadratic problem.
After you solve for $x$, compute $y$ by using $y=3x$.
Edit:
From substitution, we have 
$$\frac{20x}{3x-1}+\frac{5x+2}{3}=12$$
Multiply $3$ throughout:
$$\frac{60x}{3x-1}+5x+2=36$$
Multiply $(3x-1)$ throughout, we obtain:
$$60x+(5x+2)(3x-1)=36(3x-1)$$
which is a quadratic equation.
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