SOLUTION: a/x + b/y = a/2 + b/3 x - y = -1 Solve this with Substitution Method?

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Question 875432: a/x + b/y = a/2 + b/3
x - y = -1

Solve this with Substitution Method?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify the first equation, and then use substitution to solve the system.

6xy is the common denominator, which you should multiply both sides:
6ay%2B6bx=3axy%2B2bxy

Simpler second equation is also x=y-1, substitute into the first now simplified equation.
6ay%2B6b%28y-1%29=3a%28y-1%29y%2B2b%28y-1%29y
6ay%2B6by-6b=3ay%5E2-3ay%2B2by%5E2-2by
3ay%5E2%2B2by%5E2-3ay-2by-6ay-6by%2B6b=0
3ay%5E2%2B2by%5E2-9ay-8by%2B6b=0
highlight_green%28%283a%2B2b%29y%5E2-%289a%2B8b%29y%2B6b=0%29, a quadratic equation in the variable, y, on which you can use the general solution for a quadratic equation. Many symbols to write, and doing this is much more fast and comfortable on paper than by typing text onto this webpage.