SWBAT… Solve a system of equations using the graphing method Tues, 2/5 Agenda WU (5 min) Notes (15 min) Graphing method posters (30 min) Warm-Up: Set-up your notes – Topic is “System of Equations – Graphing Method” HW#1: Systems - Graphing

We are starting a new unit: System of Linear Equations & Inequalities SWBAT… Solve a system of linear equations using the graphing method Solve a system of linear equations using the substitution method Solve a system of linear equations using the elimination method (adding, subtracting, or multiplying) Write and solve a system of equations based on real life scenarios (application word problems) Solve a system of linear inequalities using the graphing method (~4 week unit)

What should I already know to be successful in this unit (pre-requisite skills)? Distributive property Combining like terms Solving a multi-step equation Solving a literal equation Finding the slope and y-intercept of lines Graphing lines (solving for y) Writing equations of lines in slope-intercept form Writing and finding ordered pairs Parallel lines and intersecting lines

MT = T + Th + R206 + R208 MT = Math Tutoring T = Tuesday Th = Thursday R206 = Room 206 R208 = Room 208 MT = T + Th + R206 + R208

System of Equations: Graphing Method What is a system of equations? A collection of equations involving the same set of variables. We will be dealing with two equations and two variables. x – y = 2 3y + 2x = 9

Solving Systems of Equations: Graphing Method Step 1) Write the equations of the lines in slope intercept form. Step 2) Graph each line on the same graph. Step 3) Determine the point of intersection and write this point as an ordered pair. If the two equations have no points in common, the system of equations has no solution. Parallel lines; same m and different b If the two equations represent the same line, the system of equations has infinitely many solutions. Same line; same m and same b Step 4) If there is one solution, check your work. Substitute the ordered pair for x and y in each equation.

Example Graph the system of equations. Determine whether the system has one solution, no solution, or infinitely many solutions. If the system has one solution, determine the solution and check your answer. x – y = 2 3y + 2x = 9 Step 1: Write each equation in slope-intercept form. 3y + 2x = 9 -2x -2x x – y = 2 -x -x 3y = -2x + 9 -y = -x + 2 3 3 3 -1 -1 -1 y = x – 2

Step 2: Graph each line on the same graph x y Step 3: Determine the point of intersection. (3,1). y = x – 2 This system of equations has one solution, the point (3, 1). 3 – 1 = 2 3(1) + 2(3) = 9 2 = 2 3 + 6 = 9 9 = 9 Step 4: Check your answer

Activity-System of equations – Graphing Method You and a partner will be given a system of equations to graph on poster board Directions: Solve the system using the graphing method (show work on poster) Determine the number of solutions it has If the system has one solution, name it If the system has one solution, check your answer

SWBAT… Solve a system of equations using the graphing method Wed, 2/6 Agenda WU (15 min) Conclusions about graphing method and solutions (25 min) Review HW#1 (10 min) Warm-Up: What are advantages and disadvantages to the graphing method. 1. Sample Answer: Graphing clearly shows whether a system of equations has one solution, no solution, or infinitely many solutions. However, finding the exact values of x and y from a graph can be difficult. 2. Yes. - 4 = -4 and 4 = 4

Disadvantage to graphing? Graphing clearly shows whether a system of equations has one solution, no solution, or infinitely many solutions. It’s visual! Disadvantage to graphing? Finding the exact values of x and y from a graph can be difficult. 11

Compare slope (m) and the y-intercept ( b) Types of lines Picture /Diagram Number of solutions

Compare slope (m) and the y-intercept ( b) Types of lines Picture /Diagram Number of solutions   One solution

Compare slope (m) and the y-intercept ( b) Types of lines Picture /Diagram Number of solutions Different slope (m) Same or different y-intercept (b) Intersecting lines   One solution

Compare slope (m) and the y-intercept ( b) Types of lines Picture /Diagram Number of solutions Different slope (m) Same or different y-intercept (b) Intersecting lines   One solution No Solution

Compare slope (m) and the y-intercept ( b) Types of lines Picture /Diagram Number of solutions Different slope (m) Same or different y-intercept (b) Intersecting lines   One solution Same slope (m) Different y-intercept (b)  Parallel lines  No Solution

Compare slope (m) and the y-intercept ( b) Types of lines Picture /Diagram Number of solutions Different slope (m) Same or different y-intercept (b) Intersecting lines   One solution Same slope (m) Different y-intercept (b)  Parallel lines  No Solution Infinite Solutions

Compare slope (m) and the y-intercept ( b) Types of lines Picture /Diagram Number of solutions Different slope (m) Same or different y-intercept (b) Intersecting lines   One solution Same slope (m) but Different y-intercept (b)  Parallel lines  No Solution  Same slope (m) and Same y-intercept (b) Same lines Infinite Solutions

Additional Examples Graph the system of equations. Determine whether the system has one solution, no solution, or infinitely many solutions. If the system has one solution, determine the solution.

Lines Intersect y The two equations in slope-intercept form are: x The point of intersection of the two lines is the point (3, 0). This system of equations has one solution, the point (3,0).

Lines Do Not Intersect Parallel Lines x y The two equations in slope-intercept form are: This system of equations represents two parallel lines. This system of equations has no solution because these two lines have no points in common.

Lines that are the Same y x y The two equations in slope-intercept form are: These two equations represent the same line. Therefore, this system of equations has infinitely many solutions.

HW#1: Systems-Graphing Method Answers: 1 Solution: (1, 2) 1 Solution: (-4, -2) Infinite Solutions 1 Solution: (-2, -2) Solution No Solution

Exit Slip Find the solution to the below system of equations using the graphing method. (Hint: Write each equation in slope-intercept form) How many solutions exist? Write the solution as an ordered pair. Check your answer. y – 2x = 6 -4y – 4x = 12