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?

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) (Show Source): You can put this solution on YOUR website!
Let's say you have the two equations: and

Set the two equations equal to one another

Subtract 2x from both sides

Subtract 1 from both sides

Subtract

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 of (red) and (green)

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