1. Holt Algebra 2 3-1 Using Graphs and Tables to Solve Linear Systems Section 3.1 Using Graphs and Tables to Solve Linear Systems

2. Holt Algebra 2 3-1 Using Graphs and Tables to Solve Linear Systems Homework Pg 186 #19-31, 51, 53

3. Holt Algebra 2 3-1 Using Graphs and Tables to Solve Linear Systems Use substitution to determine if the given ordered pair is an element of the solution set for the system of equations. Verifying Solutions of Linear Systems (1, 3); x – 3y = –8 3x + 2y = 9 Substitute 1 for x and 3 for y in each equation. Because the point is a solution for both equations, it is a solution of the system. 3x + 2y = 9 3(1) +2(3) 9 9 9 x – 3y = –8 (1) –3(3) –8–8 –8–8–8–8

4. Holt Algebra 2 3-1 Using Graphs and Tables to Solve Linear Systems Use substitution to determine if the given ordered pair is an element of the solution set for the system of equations. Verifying Solutions of Linear Systems (–4, ); x + 6 = 4y 2x + 8y = 1 x + 6 = 4y (–4) + 6 22 Because the point is not a solution for both equations, it is not a solution of the system. 2x + 8y = 1 2(–4) + 1 –4–4 1 Substitute –4 for x and for y in each equation. x

5. Holt Algebra 2 3-1 Using Graphs and Tables to Solve Linear Systems Use a graph and a table to solve the system. Check your answer. Solving Linear Systems by Using Graphs and Tables 2x – 3y = 3 y + 2 = x

6. Holt Algebra 2 3-1 Using Graphs and Tables to Solve Linear Systems Use a graph and a table to solve the system. Check your answer. 2y + 6 = x 4x = 3 + y

7. Holt Algebra 2 3-1 Using Graphs and Tables to Solve Linear Systems The systems of equations in Example 2 have exactly one solution. However, linear systems may also have infinitely many or no solutions. A consistent system is a set of equations or inequalities that has at least one solution, and an inconsistent system will have no solutions.

8. Holt Algebra 2 3-1 Using Graphs and Tables to Solve Linear Systems You can classify linear systems by comparing the slopes and y-intercepts of the equations. An independent system has equations with different slopes. A dependent system has equations with equal slopes and equal y-intercepts.

9. Holt Algebra 2 3-1 Using Graphs and Tables to Solve Linear Systems

10. Holt Algebra 2 3-1 Using Graphs and Tables to Solve Linear Systems Classify the system and determine the number of solutions. Classifying Linear System x = 2y + 6 3x – 6y = 18 Solve each equation for y. The system is consistent and dependent with infinitely many solutions. The equations have the same slope and y-intercept and are graphed as the same line. y = x – 3

11. Holt Algebra 2 3-1 Using Graphs and Tables to Solve Linear Systems City Park Golf Course charges $20 to rent golf clubs plus $55 per hour for golf cart rental. Sea Vista Golf Course charges $35 to rent clubs plus $45 per hour to rent a cart. For what number of hours is the cost of renting clubs and a cart the same for each course? Summer Sports Application