SOLUTION: Suppose you're solving a system of two linear equations and you arrive at an equation 0 = 0. (What an astounding fact!) What does that tell you about the relationship of the two li

Question 103927: Suppose you're solving a system of two linear equations and you arrive at an equation 0 = 0. (What an astounding fact!) 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 . If you divide both sides of by 2 you get (which is the same equation as the first one)

Now set the two equations equal to each other

Subtract 2x from both sides

Subtract 1 from both sides

Subtract

So if you set one side of an equation equal to itself, then you get the identity . This means that any x value will satisfy the equation . So there are an infinite number of solutions and the system is dependent (since the second equation is dependent on the first one)
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