# Solving Linear Equations

### What They Are & How To Solve

## Linear Equations ~ What Are They?

- A linear equation in one variable is an equation that can be written in the form ax=b.

- A linear equation in two variables is an equation that can be written in Ax+By=C

- A system of linear equations has two or more linear equations each containing two or more variables.

## Ways To Solve Linear Equations

## By Graphing

- Solve the linear equation for y
- Graph both and find where they intersect
- Check your solution by putting both numbers in the equation.
- Pro- It is usually the simplest of the ways to solve.
- Con-It is easy to not have the dot in the right place and get wrong answer. So you would probably have to get a graphing calculator.

## By Substitution

- First you need to solve for a variable.
- Substitute the expression into the other equation by putting the problem as the variable.
- Then solve the equation, which should give you one number.
- Put that number back into the original expression and solve. Write it like (x,y).
- Pro-It helps to get the exact number
- Con-At least for me, this is the most confusing method

## By Elimination

- Line up the equations.
- Eliminate a variable and solve for the other one.
- Put the found variable into one of the original equations and solve for the unknown.
- Write them as (x,y)
- Pro-You can do this pretty fast
- Con-It is easy to get confused when you use this

Q: Which is the best way to solve?

A: It really depends on the problem, but usually they will all work.

Q: How do I not get confused?

A: Just work slowly and bit by bit, don't go to fast or you'll get mixed up.

Q: What if I still don't understand?

A: Talk to your teacher, they will help you until you get it.

Solving Real World Problems with Linear Equations: An Application (Algebra I)