# How do you solve the following system?:  3x-y=4 , 3x - 5y = 2

May 18, 2018

Lettuce solve $3 x$

${1}^{s t} \text{ equation}$

$3 x - y = 4$

Transfer $y$

$3 x = 4 + y$
Just remember this value as in the next equation we have $3 x$ too

color(blue)(x=(4+y)/3

${2}^{n d} \text{ equation}$

$3 x - 5 y = 2$

Put value of $3 x$

$4 + y - 5 y = 2$

$4 - 4 y = 2$

Factorize $4$ outta it

$4 \left(1 - y\right) = 2$

Transfer $4$

$1 - y = \frac{2}{4}$

Transfer 1

$- y = \frac{1}{2} - 1$

Common Denominator

$- y = \frac{1}{2} - \frac{2}{2}$

$\cancel{-} y = \cancel{-} \frac{1}{2}$

color(Red)(y=1/2

$x = \frac{4 + y}{3}$

You get

$x = \frac{4 + \frac{1}{2}}{3}$

Common denominator

$x = \frac{\frac{8}{2} + \frac{1}{2}}{3}$

$x = \frac{9}{2} \div 3$

Invert

$x = {\cancel{9}}^{3} / 2 \times \frac{1}{\cancel{3}}$

You end up with

color(red)(x=3/2