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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.

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.

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.

(continued) Find the point of intersection. The lines intersect at (2, 5), so (2, 5) is the solution of the system. y = 2x + 1 y = 3x – 1 5 2(2) + 1 Substitute (2, 5) for (x, y). 5 3(2) – 1 5 4 + 1 5 6 – 1 5 = 5 5 = 5 Check: See if (2, 5) makes both equations true.

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 = 10 + 2 non-member = 0 + 4 T(c) c

(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.

Method 2: Using a graphing calculator. (continued) Method 2: Using a graphing calculator. First rewrite the equations using x and y. T(c) = 2c + 10 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.

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.

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

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

Activity: Systems of Equations Hint to Notebook Systems of Equations WS #1-8

Homework: WS Problems #3-8