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

##### 1 Answer

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

#ax+by=c# Then its slope is defined by#(-a/b)#

#14x+3y=12# --------------------(1)

The slope of the first line is#= (-14)/3#

#14x-3y=0#

The slope of the second line is#=(-14)/(-3)=14/3#

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