# Solving Linear Equations

## Linear Equations ~ What Are They?

• A linear equation in one variable is an equation that can be written in the form ax=b.
-a and x are constants

• A linear equation in two variables is an equation that can be written in Ax+By=C
-A, B, and C are constants, A and B are not 0

• A system of linear equations has two or more linear equations each containing two or more variables. ## 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?