How do you determine whether a linear system has one solution, many solutions, or no solution when given 4x-6y=2 and 5x+3y= 1?
1 Answer
Oct 16, 2015
Compare the slopes of the two linear equations.
Since the slopes are not equal there is exactly one solution.
Explanation:
Linear equations with either many solutions or with no solutions must have the same slope (colinear for many solutions; parallel but displaced for no solutions).
Since the slopes are different the equations are neither colinear nor parallel.