# How do you solve y= 1/x and x+5y=6 using substitution?

Jul 27, 2016

$\left(x , y\right) = \textcolor{g r e e n}{\text{(1,1)) " or " color(green)(} \left(5 , \frac{1}{5}\right)}$

#### Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} y = \frac{1}{x}$
[2]$\textcolor{w h i t e}{\text{XXX}} x + 5 y = 6$

Using [1] we can substitute $\frac{1}{x}$ for $y$ in [2]
[3]$\textcolor{w h i t e}{\text{XXX}} x + \frac{5}{x} = 6$

Multiplying both sides by $x$
[4]$\textcolor{w h i t e}{\text{XXX}} {x}^{2} + 5 = 6 x$

[5]$\textcolor{w h i t e}{\text{XXX}} {x}^{2} - 6 x + 5 = 0$
[6]$\textcolor{w h i t e}{\text{XXX}} \left(x - 1\right) \left(x - 5\right) = 0$
$\left.\begin{matrix}x = 1 & \textcolor{w h i t e}{\text{XX}} & x = 5 \\ \rightarrow y = \frac{1}{1} = 1 & \null & \rightarrow y = \frac{1}{5}\end{matrix}\right.$