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Tuesday Warmup
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Homework Check: Collect Exit ticket
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SWBAT solve systems of equations by graphing.
Math 1B Unit 0 Day 6 Objective: SWBAT solve systems of equations by graphing.
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Vocabulary Distribute Systems of Equations Handout 1
Systems of Linear Equations: Two or more linear equations using the same variables. Solutions of a System of Linear Equations: Any ordered pair in a system that makes all the equations of that system true.
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EX 1: Solve by graphing. Check your solutions.
y = 2x + 1 y = 3x – 1 y = 2x + 1 The slope is 2. The y-intercept is 1. y = 3x – 1 The slope is 3. The y-intercept is –1. Graph both equations on the same coordinate plane.
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(continued) Find the point of intersection. The lines intersect at (2, 5), so (2, 5) is the solution of the system. y = 2x y = 3x – 1 5 2(2) + 1 Substitute (2, 5) for (x, y) (2) – 1 – 1 5 = = 5 Check: See if (2, 5) makes both equations true.
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EX 2: Suppose you plan to start taking an aerobics class
EX 2: Suppose you plan to start taking an aerobics class. Non-members pay $4 per class while members pay $10 a month plus an additional $2 per class. After how many classes will the cost be the same? What is that cost? Define: Let = number of classes. Let = total cost of the classes. c T(c) Relate: cost is membership plus cost of classes fee attended Write: member = non-member = T(c) c
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(continued) Method 1: Using paper and pencil. T(c) = 2c + 10 The slope is 2. The intercept on the vertical axis is 10. T(c) = 4c The slope is 4. The intercept on the vertical axis is 0. Graph the equations. T(c) = 2c + 10 T(c) = 4c The lines intersect at (5, 20). After 5 classes, both will cost $20.
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Method 2: Using a graphing calculator.
(continued) Method 2: Using a graphing calculator. First rewrite the equations using x and y. T(c) = 2c y = 2x + 10 T(c) = 4c y = 4x Then graph the equations using a graphing calculator. Set an appropriate range. Then graph the equations. Use the key to find the coordinates of the intersection point. The lines intersect at (5, 20). After 5 classes, both will cost $20.
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Ex3: Solve by graphing. y = 3x + 2
Graph both equations on the same coordinate plane. y = 3x + 2 The slope is 3. The y-intercept is 2. y = 3x – 2 The slope is 3. The y-intercept is –2. The lines are parallel. There is no solution.
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Ex 4: Solve by graphing. 3x + 4y = 12 y = – x + 3
Graph both equations on the same coordinate plane. 3x + 4y = 12 The y-intercept is 3. The x-intercept is 4. y = – x + 3 The slope is – . The y-intercept is 3. 3 4 The graphs are the same line. The solutions are an infinite number of ordered pairs (x, y), such that y = – x + 3. 3 4
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Properties of Different Lines
Reminder: Properties of Different Lines Type of Lines Slope Y-intercept Solutions Intersecting Different Same or Different 1 solution (x,y) Parallel Same No Solution Infinite Solution
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Activity: Systems of Equations Hint to Notebook
Systems of Equations WS #1-8
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Homework: WS Problems #3-8
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