SOLUTION: Write two equations that each represents one of a pair of parallel lines. If we consider two equations as a system of equations, what is the solution set of the system? Explain

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Question 766507: Write two equations that each represents one of a pair of parallel lines. If we consider two equations as a system of equations, what is the solution set of the system? Explain
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
y = 2x + 3
y = 2x + 5

these 2 equations are parallel because they have the same slope and a different y intercept.

solve these 2 equations simultaneously using the elimination method.

you get:

y = 2x + 3 (first equation)
y = 2x + 5 (second equation)

subtract equation 2 from equation 1 to get:

0 = 0 - 2
simplify this to get:
0 = -2

all the variables have disappeared and you are left with an equation that is not true, so there is no solution to this system of equations which means the lines do not intersect at any point which means the lines have to be parallel.