Answer to Question #311227 in Algebra for johhny

Question

Substitution Method; 1. 3x-6y=4; 5x-5y=2 2. 2x+3y=3;4x-6y=4

Answer 1

$1.\\ 3x-6y=4\\5x-5y=2\\ 3x=4+6y\\ x=\frac{4+6y}{3}\\ 5\cdot\frac{4+6y}{3}-5y=2\\ 20+30y-15y=6\\ 15y=-14\\ y=-\frac{14}{15}\\ x=\frac{4+6\cdot\frac{-14}{15}}{3}=\frac{-\frac{24}{15}}{3}=-\frac{8}{15}\\ (-\frac{8}{15},-\frac{14}{15})$

$2.\\ 2x+3y=3\\4x-6y=4\\ 2x=3-3y\\ x=\frac{3-3y}{2}\\ 4\cdot\frac{3-3y}{2}-6y=4\\ 6-6y-6y=4\\ -12y=-2\\ y=\frac{2}{12}\\y=\frac{1}{6}\\ x=\frac{3-3\cdot\frac{1}{6}}{2}=\frac{\frac{5}{2}}{2}=\frac{5}{4}\\ (\frac{5}{4},\frac{1}{6})$