Section 7 – 1 Solving Systems of Equations by Graphing

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Presentation transcript:

Section 7 – 1 Solving Systems of Equations by Graphing Objectives: To solve systems by graphing To analyze special types of systems

System of Linear Equations: Two or more linear equations Example: y = 2x – 3 2x + 3y = 12 y = x – 1 y = 6x + 2 There are Three Ways to Solve a System of Linear Equations: Graphing Substitution Elimination

Solution of the System of Linear Equations: A point (ordered pair) that both lines have in common when they are graphed. This ordered pair will make ALL the equations true when it is plugged in. Is (-1, 5) a solution to the system? x + y = 4 x = -1 Is (3, -2) a solution to the system? 6x – 6y = 2 3x + 9y = -7

Example 1 Solving a System by Graphing Solve by graphing. y = 2x – 3 y = x – 1 CHECK YOUR ANSWER:

B) Solve by graphing. y = x + 5 y = -4x CHECK YOUR ANSWER:

C) Solve by graphing. 𝑦=− 1 2 𝑥+2 𝑦=−3𝑥−3 CHECK YOUR ANSWER:

D) Solve by graphing. 2y – 4x = 2 2y – 6x = -2 CHECK YOUR ANSWER:

Homework: Textbook Page 343; # 2 – 12 Even (Make sure to Check ALL answers!)

To solve systems by graphing To analyze special types of systems Section 7 – 1 Continued… Objectives: To solve systems by graphing To analyze special types of systems

Example 2 Word Problems A) Suppose you plan to start taking a kick-boxing class. Nonmembers pay $4 per class and members pay a $10 fee plus an additional $2 per class. After how many classes will the cost be the same? What is that cost?

B) Suppose you are testing two fertilizers on bamboo plants A and B, which are growing under identical conditions. Plant A is 6 cm tall and growing at a rate of 4cm/day. Plant B is 10 cm tall and growing at a rate of 2cm/day. After how many days will the bamboo plants be the same height? What will their height be?

C). Suppose you have $20 in your bank account C) Suppose you have $20 in your bank account. You start saving $5 each week. Your friend has $5 in his account and is saving $10 each week. Assume that neither you nor your friend makes any withdrawals. After how many weeks will you and your friend have the same amount of money in your accounts? How much money will each of you have?

Homework: Complete Word Problem Worksheet