How to solve this System of Polynomial Equations? I have to complete a summer packet of 90 Algebra 2 questions. I have completed 89 of them, the only one I could not get was this. I know the answer is $y = \frac {47}2$, $\frac 17$ according to WolframAlpha, but I have no idea how to reach that answer, my Algebra 2 Honors teacher couldn't figure it out.
Directions: Use substitution or linear combination to solve each system.
$$\dfrac 3{(x-1)} + \dfrac 4{(y+2)} = 2$$
    $$\dfrac 6{(x-1)} - \dfrac 7{(y+2)} = -3$$

How about this approach: It's not hard to see that $2 \cdot \left(\frac{3}{x-1}\right) = \frac{6}{x-1}$. Therefore, we can do a linear combination approach:
Add $-2$ times the first equation to the second equation. We get:
$$ \left(\frac{6}{x-1} - \frac{7}{y+2} \right) - 2 \left( \frac{3}{x-1} + \frac{4}{y+2} \right) = -3 - 2\cdot 2.$$
Simplifying gives $$\frac{-15}{y+2} =\frac{-7-8}{y+2} + \frac{6-6}{x-1} = -7.$$
Can you take it from here?
