Chapter 4: Systems of Equations and Inequalities Section 4.3: Solving Linear Systems Using Graphs

Goals: To find the solution of a linear system graphically and to determine if the system is consistent dependent, consistent independent, or inconsistent

Section 4.3: Solving Linear Systems Using Graphs System of Equations – two or more equations with the same variables. To solve, find the ordered pair that satisfies ALL of the equations

Section 4.3: Solving Linear Systems Using Graphs Example 1 Solve the system of equations by graphing. x + y = 3 -2x + y = -6

Section 4.3: Solving Linear Systems Using Graphs Example 2 Solve the system of equations by graphing. x – 2y = 0 x + y = 6

Section 4.3: Solving Linear Systems Using Graphs Classifying Systems Consistent – at least one solution Independent – exactly one solution Dependent – infinite solutions Inconsistent – no solutions

Section 4.3: Solving Linear Systems Using Graphs

Example 4 Graph the system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent. x – y = 5 x + 2y = -4

Section 4.3: Solving Linear Systems Using Graphs Example 5 Graph the system of equations and describe it as consistent and dependent, consistent and independent, or inconsistent. 9x – 6y = -6 6x – 4y = -4

Section 4.3: Solving Linear Systems Using Graphs Example 6 Graph the system of equations and describe it as consistent and independent, consistent and dependent, and inconsistent. 15x – 6y = 0 5x – 2y = 10

Section 4.3: Solving Linear Systems Using Graphs Homework: Practice Exercises: Pg. 157 #2-28 (even)