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3-1 Using Graphs and Tables to Solve Linear Systems You will need: -Spiral/paper to take notes -A textbook (in this corner =>) -The Pre-AP agreement if you have it signed Holt Algebra 2 3-1 Using Graphs and Tables to Solve Linear Systems A point is a solution to a system of equation if the x- and y-values of the point satisfy both equations. Use substitution to determine if the given ordered pair is an element of the solution set for the system of equations. x – 3y = –8 (1, 3); 3x + 2y = 9 x – 3y = –8 3x + 2y = 9 (1) –3(3) –8 3(1) +2(3) 9 –8 –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 Recall that you can use graphs or tables to find some of the solutions to a linear equation. You can do the same to find solutions to linear systems. Holt Algebra 2 3-1 Using Graphs and Tables to Solve Linear Systems Example 2A: Solving Linear Systems by Using Graphs and Tables Use a graph and a table to solve the system. Check your answer. 2x – 3y = 3 y+2=x Solve each equation for y. y= x–1 y= x – 2 Holt Algebra 2 3-1 Using Graphs and Tables to Solve Linear Systems Example 2A Continued On the graph, the lines appear to intersect at the ordered pair (3, 1) 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 Example 3A: Classifying Linear System Classify the system and determine the number of solutions. x = 2y + 6 3x – 6y = 18 Solve each equation for y. y= x–3 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 Homework Pg. 187-188 # 28,29,35,37,40,45 Holt Algebra 2