# How do solve the following linear system?:  x + 3y = 9 , x-2y=8 ?

Feb 9, 2016

Solution is $x = 8 \frac{2}{5} \mathmr{and} 8.4$ and $y = \frac{1}{5} \mathmr{and} 0.2$

#### Explanation:

In these pair of linear equations, you can eliminate $x$ simply by subtracting second equation from first, which gives

$\left(x + 3 y\right) - \left(x - 2 y\right) = 9 - 8$ i.e.

$5 y = 1$ or $y = \frac{1}{5}$ or $y = 0.2$

Putting this in second equation $x - 2 \left(\frac{1}{5}\right) = 8$ or

$x = 8 + \left(\frac{2}{5}\right)$ i.e. $x = 8.4$

Hence solution is $x = 8 \frac{2}{5} \mathmr{and} 8.4$ and $y = \frac{1}{5} \mathmr{and} 0.2$