Systems of Linear Equations Vocabulary

The equations are exactly the same. (SAME slope AND SAME y-intercept). The lines intersect at EVERY point.​ ​

• Infinitely Many Solutions

• No Solution

• One Solution

A system of equations in which the equations have DIFFERENT slopes and intersect at ONE point.

• One Solution

• Infinitely Many Solutions

• No Solution

two or more linear equations with the same variables

• piecewise defined function

• linear inequality

• solution to a linear inequality

• boundary line

• system of linear equations

A method to solve a system. One equation is solved for one of the variables then the expression for that variable is substituted into the other equation

• substitution method

• elimination method

• coincident lines

• parallel lines

• slope intercept form

A method to solve a system. Two equations are combined to eliminate one variable.

• substitution method

• elimination method

• coincident lines

• parallel lines

• slope intercept form

Lines that occupy the same location, pass through the same set of ordered pairs and intersect infinitely many times.

• substitution method

• elimination method

• coincident lines

• parallel lines

• slope intercept form

Systems that produce two distinct lines when graphed

• Independent System

• Dependent System

• Inconsistent Systems

• Consistent Systems

• Solution Region

Systems that produce coincident lines when graphed

• Independent System

• Dependent System

• Inconsistent Systems

• Consistent Systems

• Solution Region

Systems that have no solution when graphed

• Independent System

• Dependent System

• Inconsistent Systems

• Consistent Systems

• Solution Region

Systems that have at least one solution when graphed

• Independent System

• Dependent System

• Inconsistent Systems

• Consistent Systems

• Solution Region