# How to determine the number of solutions in a linear system without solving: 14x + 3y = 12 and 14x - 3y = 0?

Nov 29, 2015

The system of equations have one solution.

#### Explanation:

The system of equations have one solution because their slopes are not equal. There is a chance for the two lines to cut each other.

If a straight line equation is in the form of

$a x + b y = c$ Then its slope is defined by $\left(- \frac{a}{b}\right)$
$14 x + 3 y = 12$ --------------------(1)
The slope of the first line is $= \frac{- 14}{3}$

$14 x - 3 y = 0$
The slope of the second line is $= \frac{- 14}{- 3} = \frac{14}{3}$

Their slopes are different. They will cut each other. Hence they have one solution.