System of linear equations

Definition

A system of linear equations consists of two or more linear equations involving the same set of variables. The solutions to the system are the points where the graphs of these equations intersect.

5 Must Know Facts For Your Next Test

1. A solution to a system of linear equations is an ordered pair that satisfies all equations in the system.
2. Graphically, the solution is the point(s) where the lines intersect.
3. Systems can have one solution (intersecting lines), no solution (parallel lines), or infinitely many solutions (coincident lines).
4. The substitution method involves solving one equation for one variable and substituting this expression into another equation.
5. The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variables.

Review Questions

• What are the possible outcomes for a system of linear equations in two variables?
• How does graphing help in finding solutions to a system of linear equations?
• Describe the substitution and elimination methods for solving systems of linear equations.

Related terms

Linear Equation: An equation that makes a straight line when it is graphed. It has no variables raised to any power other than one.

Intersection Point: The point where two or more graphs meet, representing a shared solution among them.

Parallel Lines: Lines in a plane that never meet. They have the same slope but different y-intercepts.