3 1 Using Graphs and Tables to Solve

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

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

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

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

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

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

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

3 -1 Using Graphs and Tables to Solve Linear Systems Summer Sports Application 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? Holt Algebra 2