6-3: ELIMINATION USING ADDITION AND SUBTRACTION

1) Use substitution to solve the system:

x = -2y x + y = 4

1 2 3 4

55%

5%10%

30%

1. (8, -4)2. (2, -2)3. Infinite solutions4. No solution

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2) Use substitution to solve the system:

4x – y = 2 ¼ y = x – ½

1 2 3 4

10%

14%

38%38%1. (1, 2)2. (2, 6)3. Infinite solutions4. No solution

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3) The sum of two numbers is 31. The greater number is 5 more than the lesser number. What are the two numbers?

1 2 3 4

0% 0%5%

95%1. 10 & 152. 13 & 183. 14 & 194. 16 & 21

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4) Adult tickets to a play cost $5 and student tickets cost $4. On Sunday, the adults that paid accounted for seven more than twice the number of students that paid. The income from ticket sales was $455. How many students paid?

1 2 3 4

0%

19%

38%43%1. 130

2. 903. 804. 30

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Participant Scores

4 Daniel Helper

3 Andrew Duncan

3 Anya Augin

3 Naomi Bervin

3 Alexander Vendress

6-3: Elimination using Addition/Subtraction

Last week, we solved equations using substitution

This week, we concentrate on elimination1. Write the system so like terms with the

same or opposite coefficients are aligned2. Add or subtract the equations, eliminating

one variable. Then solve the equation3. Substitute the value from Step 2 into one

of the equations and solve for the other variable. Write the solutions in (x, y) order

6-3: Elimination using Addition/Subtraction

Example Using Addition -3x + 4y = 12

3x – 6y = 18 -2y = 30 y = -15

3x – 6(-15) = 18 Substitute x = -15 3x + 90 = 18 Multiply -6(-15) 3x = -72 Subtract 90 both sides x = -24 Divide 3 both sides

(-24, -15) is the solution

Ex 1: Use elimination to solve the system

3x – 5y = 1 2x + 5y = 9

1 2 3 4

5%0%0%

95%1. (1, 2)2. (2, 1)3. (0, 0)4. (2, 2)

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6-3: Elimination using Addition/Subtraction Write and solve a system

Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers

4x – 3y = 122x + 3y = 6

6x = 18 x = 3

2(3) + 3y = 6 Substitute x = 3 6 + 3y = 6 2(3) = 6 3y = 0 Subtract 6 each side y = 0 Divide 3 each side

(3, 0) is the solution

Ex 2: Four times one number added to another number is -10. Three times the first number minus the second number is -11. Find the numbers.

1 2 3 4

84%

0%5%

11%

1. -3 & 22. -5 & -53. -5 & -64. 1 & 1

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6-3: Elimination using Addition/Subtraction

Example Using Subtraction 4x + 2y = 28 4x + 2y = 28

4x – 3y = 18 -4x + 3y = -18 5y = 10 y = 2

4x + 2(2) = 28 Substitute y = 2 4x + 4 = 28 Multiply 2(2) 4x = 24 Subtract 4 both

sides x = 6 Divide 4 both sides

(6, 2) is the solution

Ex 3: Use elimination to solve the system

9x – 2y = 30 x – 2y = 14

1 2 3 4

5%

95%

0%0%

1. (2, 2)2. (-6, -6)3. (-6, 2)4. (2, -6)

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6-3: Elimination using Addition/Subtraction Write and solve a system

A hardware store earned $956.50 from renting ladders and power tools last week. The store charged 36 days for ladders and 85 days for power tools. This week the store charged 36 days for ladders, 70 days from power tools, and earned $829. How much does the store charge per day for ladders and power tools?

36x + 85y = 956.5036x + 70y = 829

15y = 127.50 y = 8.5

36x + 70(8.5) = 829 Substitute y = 8.5 36x + 595 = 829 70(8.5) = 595 36x = 234 Subtract 595 each side x = 6.5 Divide 36 each side

$6.50 for ladders, $8.50 for power tools

Ex 4: Marcus and Anisa participated in a walk-a-thon. Marcus walked 11 miles and Anisa walked 13. Together, they raised $523.50. After lunch, Marcus walked 14 miles and Anisa walked 13. In the afternoon they raised $586.50. How much did each raise per mile?

1. Marcus: $22.00Anisa: $21.65

2. Marcus $21.00Anisa: $22.50

3. Marcus: $24.00Anisa: $20.00

4. Marcus: $20.75Anisa: $22.75

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6-3: Elimination using Addition/Subtraction

Assignment Page 353 1 – 23, odds