SOLUTION: Suppose you're solving a system of 2 linear equations and you come up with the equation 0 = -5. What does that tell you about the relationship of the two lines?

Algebra ->  Linear-equations -> SOLUTION: Suppose you're solving a system of 2 linear equations and you come up with the equation 0 = -5. What does that tell you about the relationship of the two lines?      Log On


   

Question 103928: Suppose you're solving a system of 2 linear equations and you come up with the equation 0 = -5. What does that tell you about the relationship of the two lines?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's say you have the two equations: y=2x%2B1 and y=2x-4

2x%2B1=2x-4 Set the two equations equal to one another


2x%2B1-2x=-4 Subtract 2x from both sides


2x-2x=-4-1 Subtract 1 from both sides


0x=-5 Subtract


0=-5 Simplify


Notice we have a contradiction (0 will never be equal to -5). Since this statement is never true, there are no solutions.


Notice if we graph the two equations, we get:


+graph%28+500%2C+500%2C+-6%2C+5%2C+-10%2C+10%2C2x%2B1%2C2x-4%29+ Graph of y=2x%2B1 (red) and y=2x-4 (green)


Notice the two lines are parallel and will never intersect. So this means the system has no solutions.