SWBAT Solve a system of equations using the
SWBAT… Solve a system of equations using the graphing method Tues, 2/5 Agenda 1. WU (5 min) 2. Notes (15 min) 3. 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 n SWBAT… 1. 2. 3. 4. 5. 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)? 1. 2. 3. 4. 5. 6. 7. 8. 9. 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 = Math Tutoring T = Tuesday Th = Thursday R 206 = Room 206 R 208 = Room 208 MT = T + Th + R 206 + R 208
System of Equations: Graphing Method n 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 3 y + 2 x = 9
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 pai for x and y in each equation.
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 3 y + 2 x = 9 Step 1: Write each equation in slope-intercept form. x–y=2 -x -x -y = -x + 2 -1 -1 -1 y=x– 2 3 y + 2 x = 9 -2 x 3 y = -2 x + 9 3 3 3
Step 2: Graph each line on the same graph y x y=x– 2 Step 3: Determine the point of intersection. (3, 1). This system of equations has one solution, the point (3, 1). 3– 1=2 3(1) + 2(3) = 9 Step 4: Check your answer 2=2 3+6=9 9=9
Activity-System of equations – Graphing Method n You and a partner will be given a system of equations to graph on poster board n Directions: Solve the system using the graphing method (show work on poster) 2. Determine the number of solutions it has 3. If the system has one solution, name it 4. If the system has one solution, check your answer 1.
SWBAT… Solve a system of equations using the graphing method Wed, 2/6 Agenda 1. WU (15 min) 2. Conclusions about graphing method and solutions (25 min) 3. Review HW#1 (10 min) Warm-Up: What are advantages and disadvantages to the graphing method.
Advantage 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.
Types of Compare slope (m) and lines the y-intercept ( b) Picture /Diagram Number of solutions
Types of Compare slope (m) and lines the y-intercept ( b) Picture /Diagram Number of solutions One solution
Compare slope (m) and Types of lines the y-intercept ( b) Picture /Diagram Number of solutions One solution Intersecting Different slope (m) lines Same or different y-intercept (b)
Types of Compare slope (m) and lines the y-intercept ( b) Picture /Diagram Number of solutions One solution Different slope (m) Intersecting Same or different y-intercept (b) lines No Solution
Types of Compare slope (m) and lines the y-intercept ( b) Picture /Diagram Number of solutions One solution Different slope (m) Intersecting Same or different y-intercept (b) lines Same slope (m) Different y-intercept (b) Parallel lines No Solution
Types of Compare slope (m) and lines the y-intercept ( b) Picture /Diagram Number of solutions One solution Different slope (m) Intersecting Same or different y-intercept (b) lines Same slope (m) Different y-intercept (b) Parallel lines No Solution Infinite Solutions
Compare slope (m) and Types of lines the y-intercept ( b) Picture /Diagram Number of solutions One solution Intersecting Different slope (m) lines Same or different y-intercept (b) Same slope (m) but Different y-intercept (b) Parallel lines Same slope (m) and Same y-intercept (b) Same lines No Solution Infinite Solutions
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.
y Lines Intersect The two equations in slopeintercept 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 y Parallel Lines The two equations in slopeintercept form are: x This system of equations represents two parallel lines. This system of equations has no solution because these two lines have no points in common.
y Lines that are the Same The two equations in slopeintercept form are: x These two equations represent the same line. Therefore, this system of equations has infinitely many solutions.
HW#1: Systems-Graphing Method Answers: 1. 2. 3. 4. 5. 6. 1 Solution: (1, 2) 1 Solution: (-4, -2) Infinite Solutions 1 Solution: (-2, -2) 1 Solution: (-3, 5) No Solution
Exit Slip 1. Find the solution to the below system of equations using the graphing method. (Hint: Write each equation in slope-intercept form) 1. How many solutions exist? Write the solution as an ordered pair. 2. Check your answer. y – 2 x = 6 -4 y – 4 x = 12
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