# How do you solve the following linear system: x - 5y = 3, 2x - 10y = -3 ?

Mar 29, 2018

the lines are parallel

They do not intersect

#### Explanation:

$x - 5 y = + 3$

$2 x - 10 y = - 3$

Here,
Differentiating line 1 wrt x
Slope of line 1 is

$1 - 5 \frac{\mathrm{dy}}{\mathrm{dx}} = 0$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{5}$
Differentiating line 2 wrt x
Slope of line 2 is

$2 - 10 \frac{\mathrm{dy}}{\mathrm{dx}} = 0$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{2}{10} = \frac{1}{5}$

the lines are parallel

They do not intersect