# Solving Systems of linear equations

### Oh the joys of algebra

## Pros and Cons

Pros: It's a visual, and it can be a simpler method when stuck.

Cons: It's only an estimate, and it is harder to show work.

Substitution

Pros: Easy with coefficient of one.

Cons: Time consuming without a coefficient of one.

Elimination

Pro: Can be the fastest way.

Cons: Can get confusing when multiplying when negatives are involved.

## The Three Methods

## Graphing Use rise and run. For example if we have y=2x-1. Go down 1 on the graph, make a point then put 2 over 1. And go up 2 then over 1, in a fraction like this 2/1. Make another point. Do not forget to connect the points. | ## Substitution One equation must be solved for a variable. So let's say we solved for x in the first equation, in the second equation we substitute x with the first equations then solve. Last we will put that solution into the first equation to solve it. Refer to picture | ## Elimination To start we have to have one negative variable and one positive variable that match. If there is not a negative simply multiply by -1. Then we solve down like an addition or subtraction problem. After this we will have an answer for the variables that match. Then replace the variable you solved for the solution and solve. Like in the example above. |

## Graphing

## Substitution

## Elimination

## Important Steps

- Solve both equations for y.
- Use rise and run.
- Check your answer by substituting for the variables.

Substitution

- Always check your work.
- Show work.

Elimination

- Always have a negative and a positive variable.
- Again check your work.
- If multiplying, make sure to change the whole equation.
- Show your work.

## Frequently Asked Questions

*Which method is easiest?*

The easiest method is substitution. Although many methods can be easier for other people. Elimination is typically the fastest method

*Which method should I use?*

Graphing can be used when both equations are solved for y and the answer can be an estimate

Substitution can be used when both equations are solved for the same variable, or have a coefficient of 1 or -1 and if either equation is solved for a variable.

Elimination can be used when one equation is positive and the other is negative.