Graphing Question

Question

(1) Label each case below as either independent or dependent and label each case as either consistent or inconsistent.

               
 Case 1: Cross lines

 

Case 2: Parallel Lines

 

Case 3: Single line

 

**I could not copy and paste the graph pictures 
 
 
 
 

Answer 1

A solution to a system of equations is a pair of X and Y values where both equations are true.  If the system has at least one solution, it is called "consistent".

 

If two lines intersect (cross), the (x,y) point where they meet is the only pair of X and Y values that fit both equations. 

Since there is only one solution, this is called "independent".

 

If two lines are coincident (one lies on top of the other), every (x,y) point on the lines satisfies both equations. Since there are an infinite number of solution points, this is called "dependent".  The (x,y) values for a solution depend on which point you choose to look at.

 

If the lines are parallel, they never cross, there is no (x,y) point that satisfies both equations.

Since there are no solutions, this is called "inconsistent".

 

Your Case 1 is two lines that intersect:  consistent, independent

Case 2 is parallel lines:  consistent, dependent

Case 3 is not a single line, but two lines that coincide:  inconsistent   (dependent/independent does not apply)