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
Alan P.
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).

#4x-6y=2# has a slope of #-4/(-6) = 2/3#

#5x+3y=1# has a slope of #-5/3#

Since the slopes are different the equations are neither colinear nor parallel.

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