This week, I learned about linear systems with substitution. When using the substitution method, you simplify one out of the two equations. To do this, you have to find the x or the y first, and then you have to add it to the second equation to find either the x value or the y value. When you are working with linear equations there will always be three possible outcomes. If both slopes of both lines is the same but the b value is not, then there won’t be a solution. If the slope is different in each equation, then there will be one solution. The final outcome is if the slope and the value of b are both the same, then the amount of solutions is infinite. To solve linear systems using the substitution method, you start by choosing one of the equations to rearrange and make it into an x= or y= equation. Next, you would substitute the answer into the x or y in the second equation and you would use brackets to do this, you will need to solve this equation. The final step to solve linear equations using substitution is to substitute the value of x or y into the rearranged equation. You can verify your equation when you’re done.

Here is an example of what using the substitution method would look like: