SOLUTION: Linear System Explain why the following linear system has no solution. y-2x=1 y=2x+3

Question 177761: Linear System
Explain why the following linear system has no solution.
y-2x=1
y=2x+3
Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Because when you put the first equation in to slope-intercept form you will see that the two lines have the same slope but different y-intercepts, therefore they are two distinct parallel lines. Parallel lines never intersect, so there cannot be a common solution to both equations, meaning the solution set of the system is the empty set.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Explain why the following linear system has no solution.
y-2x=1
y=2x+3
----------
Writing both in slope-intercept form you get:
y = 2x+1
y = 2x + 3
--------
The slopes are the same and the intercepts are different,
so thelines are parallel; they have no common point.
Cheers,
Stan H.

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