# How do you solve the simultaneous equations  y+2x=6 and y=4/x?

Mar 9, 2018

The solution sets are $\left(1 , 4\right)$ and $\left(2 , 2\right)$

#### Explanation:

We have $y + 2 x = 6$ and $y = \frac{4}{x}$. Input the second equation into the first:

$\frac{4}{x} + 2 x = 6$

$\frac{2 {x}^{2} + 4}{x} = 6$

$2 {x}^{2} + 4 = 6 x$

$2 {x}^{2} - 6 x + 4 = 0$

${x}^{2} - 3 x + 2 = 0$

${x}^{2} - x - 2 x + 2 = 0$

$x \left(x - 1\right) - 2 \left(x - 1\right) = 0$

$\left(x - 1\right) \left(x - 2\right) = 0$

$x = 1 , 2$

Inputting the first value into equation one:

$y + 2 \cdot 1 = 6$

$y + 2 = 6$

$y = 4$

Inputting the second value into equation one:

$y + 2 \cdot 2 = 6$

$y + 4 = 6$

$y = 2$

The solution sets are $\left(1 , 4\right)$ and $\left(2 , 2\right)$.