How do you determine whether a linear system has one solution, many solutions, or no solution when given y=2x+1 and y=x-2?

1 Answer
Alan P.
Oct 23, 2015

Any two lines in the Cartesian plane with different slopes intersect at exactly one location.
#y=2x+1# and #y=x-2# have different slopes
#rArr# they have one solution.

Explanation:

#y=2x+1# has a slope of #2#

#y=x-2# has a slope of #1#

A pair of straight lines in the Cartesian plane have one intersection point unless they are colinear (the same line) or parallel. Pairs of lines which are colinear or parallel have the same slope.

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