# Graphs of Linear Systems

## Key Questions

• It is possible for a system of equations to have no solution because a point on a coordinate graph to solve the equation may not exist.

This concept may seem hard to understand at first, but if you think about it, it comes easily!

The only way this can happen is if there is no intersection point, as this point would be the answer. And of course, if there is no intersection, then the lines are parallel.

Here's an example:

$y = 4 x + 19$
$y = 4 x + 7$

Here, the slopes are the same, so the lines are parallel and never intersect. That being said, there is no solution to this problem!

Hope this helps!

• I assume that you are working with a linear system with two variables here. If the graphs of the equations happen to be identical, then we know that the system has infinitely many solutions since there are infinitely many intersection points between the lines, and those intersection points represent the solutions of the system.

I hope that this was helpful.

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