Question

Solve for y in terms of x

Answer 1

let's first off notice the LCD of the denominators, hmmmm so we have denominators of 5, 3 and 13, hmmm oddly enough all those fellows are prime numbers, so the LCD will just be their product, namely 5*3*13, well, let's multiply both sides by that LCD to do away with the denominators firstly.

$\bf \cfrac{7}{5}y+\cfrac{2}{3}x=\cfrac{11}{13}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{5\cdot 3\cdot 13}}{(5\cdot 3\cdot 13)\left( \cfrac{7}{5}y+\cfrac{2}{3}x \right)}=(5\cdot 3\cdot 13)\left( \cfrac{11}{13} \right) \\\\\\ (3\cdot 13)(7y)+(5\cdot 13)(2x)=(5\cdot 3)(11)\implies 39(7y)+65(2x)=15(11) \\\\\\ 273y+130x=165\implies 273y=165-130x\implies y=\cfrac{165-130x}{273}$