October 5 th October 9 th. Unit 2: Equations & Inequalities

Transcription

1 Algebra I: Week 6 Math Packet October 5 th October 9 th Unit 2: Equations & Inequalities

2 Jump Start Directions: Answer the Regents question below to the best of your ability. Solve the inequality below to determine and state the smallest possible value for x in the solution set Systems of Equations When you are given two equations and asked to find the solution set, you are being asked to find what solutions they have in common. We call this a system of equations. Like systems of inequalities, systems of equations will have two variables. There are three ways to solve systems of equations. 1 Graphically 2 Substitution algebraically 3 Elimination algebraically Solving Systems of Equations Graphically Solving systems of equations graphically is similar to solving systems of inequalities. Step 1: Get the y by itself on one side of the equation Step 2: Graph each equation on your calculator and copy down the table. Step 3: Solution is the point where the two graphs intersect. There is no shading! 1

3 Most of the time you will be asked to find the solution of systems of equations algebraically. Next we will learn two ways of solving systems of equations algebraically. 2

4 Solving Systems of Equations Algebraically Substitution 2 + = =12 Two Algebraic Methods Elimination 2 + = =12 Step One: Make at least one equation say Step Two: the whole expression in for y in the other equation. Step Three: Follow rules for solving equations for. Step Four: Plug what you get for x into an in either equation to solve for y! Step Five: Write the solution as an pair. Step One: Find an easy to multiply by to make one coefficient match in both equations. Step Two: Eliminate a variable by adding or subtracting. Same sign,. Different sign,. Step Three: Follow rules for solving equations to solve for the variable. Step Four: Plug in what you get to solve for the second variable. Step Five: Write the solution as an pair. 3

5 Practice! Solve the following Systems of Equations. Use the substitution method for two and the elimination method for two. 4 + = 5 +4 = = =9 =4 1 = =2 +1 =7 4

6 Jump Start Solve the systems of equations below using both algebraic methods. + = + = Substitution Elimination 5

7 Solving Systems of Equations Practice Part A Directions: Solve each systems of equations by substitution + = = + = = = + = + = + = 6

8 Part B Directions: Solve each systems of equations by elimination = + = + = = = + = = = 7

9 Part C Directions: Identify the solution to the systems of equations shown on the graphs below. *Remember: the solution should be written as an ordered pair! Solution: Solution: 8

10 Jump Start Directions: Answer the Regents questions below about systems of equations as best as you can. Use your annotating skills after you read the problem once! During the 2010 season, football player McGee s earnings, m, were million dollars more than those of his teammate Fitzpatrick s earnings, f. The two players earned a total of 3.95 million dollars. Which system of equations could be used to determine the amount each player earned, in millions of dollars? Writing & Solving Systems of Equations Example 1 Samantha went to a concession stand and bought three pretzels and four sodas and paid a total of $11.25 for them. Rita went to the same stand and bought five pretzels and two sodas and paid a total of $8.25. Write and solve a system of equations for the situation. 9

11 Example 2 A local theater is showing an animated movie. They charge $5 per ticket for a child and $12 per ticket for an adult. They sell a total of 342 tickets and make a total of $2550. Let c represent the number of children s tickets sold and a represent the number of adult tickets sold. Write and solve a system of equations that represents the situation. Example 3 A catering company is setting up tables for a big event that will host 764 people. When they set up the tables they need 2 forks for each child and 5 forks for each adult. The company ordered a total of 2992 forks. Set up a systems of equations to find out how many of each attended the event. Example 4 Ilida went to Minewaska State Park one day this summer. All of the people at the park were either hiking or bike riding. There were 178 more hikers than bike riders. If there were a total of 676 people at the park, how many were hiking and how many were riding their bikes? 10

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13 Week 6 Homework Directions: Solve the following Systems of Equations algebraically using either method. 7 4 = =22 2 = = = = = = 10 12