System of linear equations

Definition

A system of linear equations is a set of two or more linear equations with the same variables. The solutions to the system are the values of the variables that satisfy all equations simultaneously.

5 Must Know Facts For Your Next Test

1. A system of linear equations can have one unique solution, infinitely many solutions, or no solution.
2. Graphically, each equation in a system represents a line, and the solution is where these lines intersect.
3. The most common methods for solving systems are graphing, substitution, and elimination.
4. If the system has no solution, the lines are parallel and never intersect.
5. If the system has infinitely many solutions, the lines coincide (are identical).

Review Questions

• What does it mean if a system of linear equations has no solution?
• Describe how you would solve a system of linear equations using the substitution method.
• How can you determine if a system of linear equations has one unique solution by graphing?

Related terms

Linear Equation: An equation that makes a straight line when it is graphed. It typically has the form $ax + by = c$.

Substitution Method: A method for solving systems of equations where one equation is solved for one variable in terms of others and then substituted into another equation.

Elimination Method: A method for solving systems where you add or subtract equations to eliminate one variable, making it easier to solve for other variables.