Vocabulary

Solution: A solution to a system of equations is the value of the variables that make all the equations TRUE.

System: A system is two or more objects that come together to make a group. 

System of Linear Equation: A collection of linear equations involving the same set of variables.

Concept

Identify the type of solution to systems.

Rules

One Solution: The solution to the system will be the point where the two lines intersect.

No Solution: If the system of linear equations have the same slope, the lines are parallel and will never intersect. The system will have no solution.

Infinite Solutions: If the two lines have the same y-intercept and the slope, they are actually in the same exact line. The system of linear equations will have infinite solutions.

Example

How many solutions does this system have?

Solution

The graphs contain the same slope, and so the lines are parallel and will never intersect. The system will have no solution.

Pre-requisite Skills

Write Linear Equations (8.3.6)

Graphing Lines Using Intercepts (8.3.5)

Slope-intercept Form of an Equation (8.3.4)