SOLUTION: hello how do i determine whether each system is independent, inconsistene, or dependent: y = 3x

SOLUTION: hello how do i determine whether each system is independent, inconsistene, or dependent: y = 3x - 5 y = 3x + 2 thank you

Question 62279This question is from textbook
: hello
how do i determine whether each system is independent, inconsistene, or dependent:
y = 3x - 5
y = 3x + 2
thank you This question is from textbook

Answer by funmath(2933) (Show Source): You can put this solution on YOUR website!
how do i determine whether each system is independent, inconsistent, or dependent:
y = 3x - 5
y = 3x + 2
Notice that these lines are in slope intercept form: , where m=slope and (0,b)=y-intercept.
:
The slope of both lines is m=3, but their y-intercepts are different, (0,-5) and (0,2). That means that these are two different lines (because their y-intercepts are different). When the lines are different, they are independent. However, their slopes are the same so they are parallel lines that will never intersect. That means they have no soltuion and are therefore inconsistent.
:
If the slopes are the same and they have the same y-intercept after simplifying, they are graphically the same line, dependent. They have infinitely many soltuions, so they are consistent.
:
If their slope are different after simplification, then they are differrent lines (independent). And have one soltuion (consistent).
Happy Calculating!!!
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