Is the system inconsistant or dependent

Question

If the system does not have a single ordered pair as a solution, state whether the system is inconsistant or dependent.

 

3x+y=-13

2x+4y=-2

Answer 1

Understand that inconsistent mean that you have 2 lines and they overlap each other completely. One could say that the two lines are indistinct with respect to one another in that if I were to put one ruler over the other, you as a bird cannot see that there are actually two rulers from the top. 

Dependent means that you have essentially two lines that never intersect (or cross) one another. This is completely opposite with respect to inconsistent systems.

Problem: 

3x+y=-13

2x+4y=-2

Step 1: Solve for y in each equation

3x+y=-13 becomes y=-13 - 3x

2x+4y=-2 becomes y=(-0.5)x-(0.5)

Step 2: If this was a dependent system, then the two y values equal one another

-13-3x=-0.5x-0.5

Step 3: Solve for x

-2.5x=12.5

x=5

Notice that these two equations/lines cross ONLY at 1 "x" value which you have received here unlike an inconsistent (which never crosses) or dependent (which shares all x values NOT just one) system. Hence this is an independent system (that is not provided in the options you have written). This type of system suggests that you have two lines that cross only one time and have just one "x" value in common.