# How do you solve the following system using substitution?: 5x-y=3, 4y-x=1

May 15, 2018

Solve one equation for one variable

#### Explanation:

Take one of the equations and solve for either x or y
$4 y - x = 1 \implies x = 4 y - 1$

Plug into the other equation for x
$5 \left(4 y - 1\right) - y = 3$

Solve
$20 y - 5 - y = 3$

$19 y = 8$

$y = \frac{8}{19}$

Plug y into original equation to find $x$

$4 \left(\frac{8}{19}\right) - x = 1$

$\frac{32}{19} - x = 1$

$x = \frac{13}{19}$

May 15, 2018

$x = \frac{13}{19}$ and $y = \frac{8}{19}$

#### Explanation:

show below:

$5 x - y = 3$...............1

$4 y - x = 1$................2

from the equation 1

$y = 5 x - 3$.............3

put 3 in 2

$4 \left(5 x - 3\right) - x = 1$

$20 x - 12 - x = 1$

$19 x = 13$

$x = \frac{13}{19}$

$y = 5 \left(\frac{13}{19}\right) - 3 = \frac{65}{19} - 3 = \frac{65 - 57}{19} = \frac{8}{19}$