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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?

1 Answers 1

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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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    Thanks! Yes I tried that but end up with a cubic equation. – 2017-01-14
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    Oh nevermind, I've got it! Substituted y = -3x – 2017-01-14
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    Hi, I made a mistake just now, should be $y=3x$. – 2017-01-14