 # Systems of Equations

Related Topics:
Common Core (Algebra)
Common Core for Mathematics

Examples, solutions, videos, and lessons to help High School students learn how to solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

### Suggested Learning Targets

• Solve systems of equations using graphs.
• Solve systems of equations using the elimination method (sometimes called linear combinations).
• Solve a system of equations by substitution (solving for one variable in the first equation and substitution it into the second equation).
Common Core: HSA-REI.C.6

Solving Systems of Equations Graphically
CCSS A.REI.6 - Solving Linear Systems by Graphing A.REI.6-1 - Solve Linear Systems by Graphing

Applications Involving Systems of Equations
Example:
1) Find the two numbers for which the sum is 93 and the difference is 9.
2) The perimeter of a rectangle is 160 yd. The width is 4 more than half the length. Find the length and the width.
3) Sunset rents an 18 ft truck for \$49.95 plus 75 cents per mile. Cactus rents a 18 ft van for \$59.95 plus 50 cents per mile. For what millage is the cost the same?
Ex: System of Equations Application - Coin Problem
This video explains how to solve an application problem using a system of equations.
Examples:
A woman has 21 coins in her pocket, all of which are dimes and quarters. If the total value of her change is \$3.90, how many dimes and how many quarters does she have?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.  