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.


Pros: Easy with coefficient of one.

Cons: Time consuming without a coefficient of one.


Pro: Can be the fastest way.

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

The Three Methods

Important Steps


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


  • Always check your work.
  • Show work.


  • 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.