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

Algebra ->  Linear-equations -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Let's say you have the two equations y=2x%2B1 and 2y=4x%2B2. If you divide both sides of 2y=4x%2B2 by 2 you get y=2x%2B1 (which is the same equation as the first one)


Now set the two equations equal to each other

2x%2B1=2x%2B1


2x%2B1-2x=1 Subtract 2x from both sides


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


0=0 Subtract


So if you set one side of an equation equal to itself, then you get the identity 0=0. This means that any x value will satisfy the equation y=2x%2B1. So there are an infinite number of solutions and the system is dependent (since the second equation is dependent on the first one)