If you are given a graph with a system of linear equations, you need to be able to look at the graph and determine how many solutions there should be.

Let’s look at these graphs.

Example 1
a graph of 2 parallel lines is shown.

 

What appears to be the number of solutions to this system?

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Check Your Answer

The lines are parallel so there is no intersection and no solution.Close Pop Up
Example 2
a graph of 2 lines intersecting is shown.

 

What appears to be the number of solutions to this system?

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Check Your Answer

The lines are intersecting so there is one intersection point.Close Pop Up

 

Example 3
a graph of 2 lines intersecting is shown.

 

 

What appears to be the number of solutions to this system?

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Check Your Answer

The lines are coinciding so there are infinite intersection points.Close Pop Up