# Systems of Equations

### The many different ways to solve them!

## What are Systems of Equations?

A system of equations is a collection of two or more equations with a same set of unknowns. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system. The equations in the system can be linear or non-linear.

How to solve substitution video O_o

## Solving Systems with Graphing To solve systems using graphing, first you need to change the equations into slope intercept form. Once that is done, graph "B" the y intercept for each equation. From those points use the "x" with rise over run to find the point. Wherever the lines intersect is your intersection point. | ## Solving Systems with Substitution To solve systems using Substitution you need to isolate x or y making it slope intercept form. Then use the opposite side of the equation and plug it into the other equation. Then solve. | ## Solving Systems with Elimination To solve systems using Elimination you need to eliminate a variable to find one variable. After finding its value, plug it into an equation to find the other variable. Then you have your points. |

## Solving Systems with Graphing

To solve systems using graphing, first you need to change the equations into slope intercept form. Once that is done, graph "B" the y intercept for each equation. From those points use the "x" with rise over run to find the point. Wherever the lines intersect is your intersection point.

## Solving Systems with Substitution

To solve systems using Substitution you need to isolate x or y making it slope intercept form. Then use the opposite side of the equation and plug it into the other equation. Then solve.

## More elimination This is another problem using elimination. | ## Writing a System When using word problems, this is simply writing the equation from a word problem! | ## Word Problems Use any of the systems of equations methods to solve a word problem. |

## Which Methods are best for different situations?

When you see two standard form equations that you need to solve, thats when its best to use elimination. When you see one slope intercept and one standard, its easiest to use substitution. Then when two slope intercept form equations show up, stick with graphing.

## Infinite solutions When two lines are the same and every point they touch is an intersection. | ## No solution When two lines are parallel and never have an intersection. | ## One solution When two lines intersect at one point. |