How to Solve Systems of Linear Equalities

Linear systems require you to solve for the common x, y coordinate among two or more equations. The term equality means each equation uses an = sign. There are several methods of solving linear equality systems, but the two most popular are substitution and elimination. Elimination isn’t always an option, so this tutorial will cover substitution.

Things You'll Need

• Graph paper

Instructions

1. Write down your system.

2. Solve one of the equations for y.

3. Substitute your solved equation in place of y in another equation. This will allow you to solve for the value of x.

4. Substitute the value of x in one of your original equations to solve for y.

5. Graph your solved x, y coordinate if required.

6. Set up a table of values for each equation to graph lines. The lines will meet at the point you found in Step 4.

Tips & Warnings

• You can choose any points you want in your table of values. Choose at least three points. You can use the point from Step 4 as one of your points.

• Always double-check your work by placing the solved x and y values into each equation.

Resources

• Ways to Solve Linear Systems
• Examples of Linear Systems