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 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.
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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)