# How do you solve x - 4y - 1 = 0 and x + 5y - 4 = 0  using substitution?

Mar 20, 2016

The solutions are:

color(green)(x = 7/3
color(green)( y = 1/ 3

#### Explanation:

$x - 4 y - 1 = 0$
$x - 4 y = 1$
color(green)(x= 1 + 4y  ..........equation $\left(1\right)$

$x + 5 y - 4 = 0$
$x + 5 y = 4$.............equation $\left(2\right)$

Substituting equation $\left(1\right)$ in $\left(2\right) :$

$\textcolor{g r e e n}{1 + 4 y} + 5 y = 4$

$1 + 9 y = 4$

$9 y = 4 - 1$

$9 y = 3$

 y = 3 / 9 = color(green)(1/ 3

Finding the value of $x$ from equation $\left(1\right)$:
color(green)(x= 1 + 4y

$x = 1 + 4 \cdot \left(\frac{1}{3}\right)$

$x = 1 + \left(\frac{4}{3}\right)$

$x = \frac{3}{3} + \left(\frac{4}{3}\right)$

color(green)(x = 7/3