1. 5-5B Linear Systems and Problems Solving Algebra 1 Glencoe McGraw-HillLinda Stamper

2. Graphing – can provide a useful method for estimating a solution and to provide a visual model of the problem. Substitution – requires that one of the variables be isolated on one side of the equation. It is especially convenient when one of the variables has a coefficient of 1 or –1. Elimination Using Addition –convenient when a variable appears in different equations with coefficients that are opposites. Elimination Using Subtraction –convenient if one of the variables has the same coefficient in the two equations. Elimination Using Multiplication –can be applied to create opposites in any system. Ways to Solve a System of Linear Equations

3. 1) Write two sets of labels, if necessary (one set for number, one set for value, weight etc.) 2) Write two verbal models. (Given in problem.) 3) Write two algebraic models - equations. (Translate from sentences.) 4) Solve the linear system. 5) Write a sentence and check your solution in the word problem. Solving Word Problems Using A Linear System

4. Let m = Meg’s age Meg’s age is 5 times Jose’s age. The sum of their ages is 18. How old is each person? m = Let j = Jose’s age Assign Labels. Choose a different variable for each person. Write an equation for each of the first two sentences. m + j = 18 Solve the system of equations. Sentence. Jose is 3 and Meg is 15. How old is Meg? = 5j

5. The length of a rectangle is 1 m more than twice its width. If the perimeter is 110 m, find the dimensions. let w = width let l = length Formula length width The width is 18 m and the length is 37 m. =

6. Example 1 A class has a total of 25 students. Twice the number of girls is equal to 3 times the number of boys. How many boys and girls are there in the class? Assign Labels. Choose a different variable for each type of person. Let g = # of girls g + b = 25 Let b = # of boys Write an equation for each of the first two sentences. 2g There are 15 girls and 10 boys in the class. = 3b

7. Example 2 The length of a rectangle is 4 m more than twice its width. If the perimeter is 38 m, find the dimensions. 4. Solve the system. 1. Labels. let w = width let l = length 2. Translate first sentence. 3. Use perimeter formula. length width 5. Sentence. The width is 5 m and the length is 14 m. =

8. let a = # of adult tickets Example 3 Admission to the play was $2 for an adult and $1.50 for a student. Total income from the sale of tickets was $550. The number of adult tickets sold was 100 less than 3 times the number of student tickets. How many tickets of each type were sold? let s = # of student tickets Number Labels. Value Labels. let 2a = let 1.50s = value of adult tickets value of student tickets

9. let a = # of adult tickets Example 3 Admission to the play was $2 for an adult and $1.50 for a student. Total income from the sale of tickets was $550. The number of adult tickets sold was 100 less than 3 times the number of student tickets. How many tickets of each type were sold? let s = # of student tickets Number Labels. Value Labels. let 2a = let 1.50s = value of adult tickets value of student tickets = a = 3s – 100 2a2a+ 1.50s = 550 Clear the decimals. Multiply both sides by 100. The school sold 200 adult tickets and 100 student tickets.

10. let q = # of quarters Example 4 The number of quarters that Tom has is 3 times the number of nickels. He has $1.60 in all. How many coins of each type does he have? let n = # of nickels Number Labels. Value Labels. let.25q = value of quarters let.05n = value of nickels

11. let q = # of quarters Example 4 The number of quarters that Tom has is 3 times the number of nickels. He has $1.60 in all. How many coins of each type does he have? let n = # of nickels Number Labels. Value Labels. let.25q = value of quarters let.05n = value of nickels = q = 3n.25q +.05n = 1.60 Clear the decimals. Multiply both sides by 100. Tom has 6 quarters and 2 nickels.

12. Example 5 The sum of two numbers is 100. Five times the smaller number is 8 more than the larger number. What are the two numbers? Assign Labels. Let s = smaller # s + l = 100 Let l = larger # Equations. 5s The larger number is 82 and the smaller number is 18. = l + 8

13. Example 6 One number is 12 more than half another number. The two numbers have a sum of 60. Find the numbers. Assign Labels. Let x = first # Let y = second # Equations. One number is 28 and the other number is 32.

14. Example 7 If you buy six pens and one mechanical pencil, you’ll get $1 change from your $10 bill. But if you buy four pens and two mechanical pencils, you’ll get $2 change. How much does each pen and pencil cost? Assign Labels. Let p = cost of a pen 6p + m = 10 - 1 Let m = cost of a mechanical pencil Equations. 4p + 2m Pens cost $1.25 each and mechanical pencils cost $1.50 each. = 10 - 2 6p + m = 10 - 1

15. 5-A8 Handout A8.

16. WHEN THE GOING GETS TOUGH – THE TOUGH GET GOING! pay attention think, think, think ask questions work with a buddy pledge to do your homework every day do it and CORRECT IT