Solutions of Systems of Equations with Ordered Pairs

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 have at least one solution when graphed

• Independent System

• Dependent System

• Inconsistent Systems

• Consistent Systems

• Solution Region

The part of the coordinate plane in which the ordered pairs are solutions to all inequalities in a system

• Independent System

• Dependent System

• Inconsistent Systems

• Consistent Systems

• Solution Region

Systems that produce two distinct 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

How can you tell if a point is a solution to a system?

• It makes the first equation true.

• The (x,y) coordinates satisfy both equations

• It makes logical sense

• It makes neither equation negative

What point is a solution to the system of equations below?

3x + 2y = 16

7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

Will the solution (-3, -7) make the following system of equations a true statement? 
y = 4x + 5
y = x – 4

• YES

• NO

Which point is a solution to the system of equations above?

• (-2, 4)

• (-2, -4)

• (2, -4)

• (2,4)