Question 62649This question is from textbook Algebra for college students
: Hello,
solve and how to determine if the system is independent, inconsistent or dependent:
y = 3x - 5
y = 3x +2
thks!
This question is from textbook Algebra for college students
Answer by funmath(2933)   (Show Source):
You can put this solution on YOUR website! solve and how to determine if the system is independent, inconsistent or dependent:
y = 3x - 5
y = 3x +2
These lines are in slope intercept form:  , m=slope and b=y-intercept.
:
If the equations have different slopes (m) they will intersect at one point giving you one solution. These lines are independent, (my book also calls them consistent.)
:
If the equations have the same slope there is one of two possibilities.
:
1. If the slopes (m's) are the same and the y-intercepts (b's) are different, then the lines are two distinct, parallel lines that will never intersect to give you a solution. They are inconsistent because they don't have a solution. (my book also calls them independent because they are separate lines.)
2. If the slopes (m) are the same and the y-intercepts (b) are the same after simplification, the lines share all points in common giving you graphically the same line. These lines are dependent because they share all points (my book also calls them consistent because there is a solution, even if there are infinintely many solutions.
:
Hello,
solve and how to determine if the system is independent, inconsistent or dependent:
E1: y = 3x - 5
E2: y = 3x +2
:
Notice the slope m of E1 and E2 are both 3, however in E1 b=-5 and in E2 b=2. Therefore the lines are parallel and will never intersect to give you a solution. The lines are inconsistent. (my book also calls them independent because they are two distinct lines.)
:
Happy Calculating!!!!
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