7.6– PROPERTIES OF SYSTEMS OF LINEAR EQUATIONS

SYSTEMS OF LINEAR EQUATIONS

TODAYS OBJECTIVES

• Students will be able to solve problems that involve systems of linear equations in two variables graphically and algebraically, including:• Explain, using examples, why a system of

equations may have no solution, one solution, or an infinite number of solutions• Explain a strategy to solve a system of linear

equations• Solve a problem that involves a system of linear

equations

VOCABULARY

• Infinite:• endless amount or number, unlimited

•Coincident lines:• two lines that have the same graph (same slope

and y-intercept)

PROPERTIES OF LINEAR SYSTEMS

• There are three possible solution sets in a system of linear equations:• 1) One solution – Lines intersect once,

different slopes• 2) No solution – Parallel lines, same

slope, different y-intercepts• 3) Infinite solutions – same lines, same

slopes, same y-intercepts

PROPERTIES OF LINEAR SYSTEMS

PROPERTIES OF LINEAR SYSTEMS

•

PROPERTIES OF LINEAR SYSTEMS

EXAMPLE

One solution

Infinite Solutions

No Solutions

CREATING A LINEAR SYSTEM WITH 0, 1, OR INFINITE SOLUTIONS

CREATING A LINEAR SYSTEM WITH 0,1, OR INFINITE SOLUTIONS

CREATING A LINEAR SYSTEM WITH 0,1, OR INFINITE SOLUTIONS

EXAMPLE

• Create a linear system with no solutions, one solution, and infinite solutions, given the equation -6x + y = 3.• Solutions: