Systems of Equations

There are 3 types of systems of equations:

1. Consistent Independent
2. Consistent Dependent
3. Inconsistent

• Consistent Independent

This system of equations is made up of two equations that intersect and have one solution. A system can automatically be determined consistent independent if the equations have different slopes and different y interecpts. Example: y = 2x+3

                                                      y = 4x+2         


In the picture, the solution is the point where the two lines cross. They seem to interesct at (1,2) which would be the one solution to this consistent independent equation.

• Consistent Dependent

 In this type of system, the solution is all real numbers. This is because the lines overlap, so they have all of the same solutions. They overlap because they have the same slope and the same y intercept. Because of this, it is very easy to identify equations that make up a consistent dependent system. Example: y = 2x+3
                   y = 2x+3

In this picture, the two colors show that there are two lines on top of each other, clearly indicating a consistent dependent system. In this example, the system is -3x +5

• Inconsistent

In this type of system, the equations have no solutuions. This is because they have the same slope and different y intercepts, making the lines parallel. Example: y = 6x+1
                                                                                               y = 6x+7

In this picture, the lines are inconsistent because of having the same slope and different y intercepts. As shown, the system has no solutions. The green line's equation is seems to be 2x+ 5 while the red line's equation is 2x-2


These are the 3 types of systems of equations! And here are examples of all 3 once more: