# Systems of Equations

### By: Nicole Barton

## System of equations

There are three types of systems of equations, there is one answer, and two special ones. The two special ones are infinite many and no solution. When there is infinite many, that means that any number can fit into that variable, and the equation will still be equal. When there is no solution, that means that the variable will cancel each other out either way, and the equation will never be equal no matter what number you put for the variable.

## Graphing

You make it to where both equations are in slope-intercept form, then graph them to find the intersection.

## Graphing- 500

In this problem, the intersection point on the graph is (-7,4), so your answer is (-7,4).

## Elimination

When solving a system of equations using elimination, you need to first line up your variables. Then you need one of the variables from bother equations to have the same coefficient, but they are opposite (one is negative and one is positive). You then add it all together to find the variable that you didn't cancel out. Then you just substitute your answer that is equal to that variable, to find the other.

## Elimination- 500

Elimination

## Elimination- 300

## Elimination- 200

## Substitution

When solving a system of equations with the elimination method, you need to find one of your variables, and find what equation equals it. After you have found the equation the is equal to your variable, you substitute it into the other equation, to find the other variable. (If you found an equation equal to X, then you would substitute it into the other problem to find Y). After you have found the answer to one of the variables, you then substitute that into an equation to find the remaining variable.

## Substitution- 500

Substitution