## Week 14 – Math 10

This week in Math 10 we learned about Systems of linear equations.

3 different types of linear equations

– No solutions

– One solution

– Infinite Solutions

First – what is a solution of a linear equation? we can graph all proper linear equations and if we have an equation **of y=3x+4 and y=2x+3**

The solution – these two equations is the points where both of the lines when graphed touch when graphed.

No Solution – when graphed the lines would be parallel. two parallel lines never touch. You can also tell if two equations have no solution if you only look at the written equation. For example if both equations have the same slope and the y-intercepts are different, this means the equation will have no equation.

y=5x+2

y=5x+5

^ no solution. If you were to put these two equations into demos, you would end up with two parallel lines.

One Solution – when a linear equation has one solution that means when graphed, somewhere along the graph the two lines will cross, sort of like an X shape. Now when written out, if both linear equations have different slopes than that means they will cross at one point. Even if the y-intercepts are the same it doesn’t matter, only the slopes need to be different.

y=6x+3

y=8x+2

These two equations are will have at least one solution guaranteed.

Infinite Solutions – So a linear equation with infinite solutions means that when graphed, the two lines will be on top of each other. If written, you can tell two equations will have infinite solutions if the slopes are the same and the y-intercepts are the same.

y=4x+3

4x-y=-3

These two equations will have infinite solutions since they are on top of each other