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=cax+by=c Then its slope is defined by(-a/b)(−ab)
14x+3y=1214x+3y=12 --------------------(1)
The slope of the first line is= (-14)/3=−143
14x-3y=014x−3y=0
The slope of the second line is=(-14)/(-3)=14/3=−14−3=143
Their slopes are different. They will cut each other. Hence they have one solution.
