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3-1 Using Graphs and Tables to Solve Linear Systems Warm Up Write each equation in slope-intercept form. 1. 2y + 8x = 6 2. 4y – 3x = 8 3-1 Using Graphs and Tables to Solve Linear Systems LEARNING GOALS FOR LESSON 3.1 1. Verify a point is a solution to a system 2. Solve a system using a graph and a table 3. Classify the number of solutions 3-1 Using Graphs and Tables to Solve Linear Systems A System of Equations is a set of two or more equations containing two or more variables. • On the graph of the system of two equations, the Solution is the set of points where the lines intersect. 3-1 Using Graphs and Tables to Solve Linear Systems Example 1: 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 − 3y = −8 # x + 6 = 4y 1 A. 1 ,3 ; $ B. −4 , 2 ; $ %3x + 2y = 9 %2x + 8y = −4 ( ( ) € ) 3-1 Using Graphs and Tables to Solve Linear Systems Example 2: Solving Linear Systems by Using Graphs and Tables Use a graph to solve the system. Check your answer with a table. Step 1: Solve each equation for y = mx + b # y = −2x + 1 $ Step 2: Graph each equation. %y + 2 = x Step 3: Plug in points with x-values around the intersection point’s x-value to each equation to determine the final answer. Step 4: Write the SOLUTION: ( _____, _____) Equation 1 x y= Equation 2 x y= 3-1 Using Graphs and Tables to Solve Linear Systems Example 2: Solving Linear Systems by Using Graphs and Tables Use a graph to solve the system. Check your answer with a table. # y = −2x + 1 $ %y + 2 = x Equation 1 x y Equation 2 x y 3-1 Using Graphs and Tables to Solve Linear Systems Example 2: Solving Linear Systems by Using Graphs and Tables Use a graph and a table to solve the system. Check your answer. Step 1: Solve each equation for y = mx + b #x − y = 2 % A. $ 3 1 y = x − % & 2 2 Step 2: Graph each equation in the calculator. 1. Push Y= 2. Type in the 1st equation into Y1 and the 2nd equation into Y2. 3. Push GRAPH 4. If you have trouble seeing the graph push ZOOM and choose option 0: ZoomFit or 6:ZStandard Step 3: Pull up the table on your calculator. 1. Push 2nd and then GRAPH. 2. Scroll to where you think the intersection point is. OR Step 3: Find the intersection point from the graph. 1. Push 2nd and then TRACE then choose option 5: intersect. 2. Press ENTER 3 times and it will give you the intersection point. Step 4: Write the SOLUTION: ( _____, _____) 3-1 Using Graphs and Tables to Solve Linear Systems Example 2: Solving Linear Systems by Using Graphs and Tables Use a graph and a table to solve the system. Check your answer. #x − y = 2 % A. $ 3 1 y = x − % & 2 2 #2y + 6 = x B. $ % y = 4x − 3 € 3-1 Using Graphs and Tables to Solve Linear Systems Consistent/ Inconsistent Dependent/ Independent Exactly One Solution Infinitely Many Solutions No Solutions Consistent and Independent Consistent and Dependent Inconsistent Are NOT = Can be = or NOT = Are = Are = Are = Are NOT = Looks Like Slopes y-intercepts 3-1 Using Graphs and Tables to Solve Linear Systems Example 3: Classifying Linear System Classify the system and determine the number of solutions. #x − y = 2 A. % $ 3 1 %y = x − & 2 2 B. € # 1 y = x −3 % % 2 $ %y = 1 x − 2 % & 2 "2 y = x − 4 $ 1 C. # y= x−2 $ % 2