6-3: ELIMINATION USING ADDITION AND SUBTRACTION

1) Use substitution to solve the system: x = -2yx + y = 4 1. (8, -4) 2. (2, -2) 3. Infinite solutions 4. No solution

2) Use substitution to solve the system: 4x – y = 2¼ y = x – ½ 1. (1, 2) 2. (2, 6) 3. Infinite solutions 4. No solution

3) The sum of two numbers is 31. The greater number is 5 more than the lesser number. What are the two numbers? & & & & 21

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?

Participant Scores 4Daniel Helper 3Andrew Duncan 3Anya Augin 3Naomi Bervin 3Alexander Vendress

6-3: Elimination using Addition/Subtraction  Last week, we solved equations using substitution  This week, we concentrate on elimination 1. Write the system so like terms with the same or opposite coefficients are aligned 2. Add or subtract the equations, eliminating one variable. Then solve the equation 3. 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 EExample Using Addition --3x + 4y = 12 3x – 6y = 18  -2y = 30 yy = -15 33x – 6(-15) = 18Substitute x = -15 33x + 90 = 18Multiply -6(-15) 33x = -72Subtract 90 both sides xx = -24Divide 3 both sides ((-24, -15) is the solution

Ex 1: Use elimination to solve the system 3x – 5y = 12x + 5y = 9 1. (1, 2) 2. (2, 1) 3. (0, 0) 4. (2, 2)

6-3: Elimination using Addition/Subtraction WWrite and solve a system F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 44x – 3y = 12 2x + 3y = 6 66x = 18 xx = 3 22(3) + 3y = 6Substitute x = 3 66 + 3y = 62(3) = 6 33y = 0Subtract 6 each side yy = 0Divide 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

6-3: Elimination using Addition/Subtraction EExample Using Subtraction 44x + 2y = 28  4x + 2y = 28 4x – 3y = 18  -4x + 3y = -18  5y = 10 yy = 2 44x + 2(2) = 28Substitute y = 2 44x + 4 = 28Multiply 2(2) 44x = 24Subtract 4 both sides xx = 6Divide 4 both sides ((6, 2) is the solution

Ex 3: Use elimination to solve the system 9x – 2y = 30x – 2y = (2, 2) 2. (-6, -6) 3. (-6, 2) 4. (2, -6)

6-3: Elimination using Addition/Subtraction WWrite and solve a system AA hardware store earned $ 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 $829. How much does the store charge per day for ladders and power tools? 336x + 85y = x + 70y = 829 115y = yy = 8.5 336x + 70(8.5) = 829Substitute y = 8.5 336x = 82970(8.5) = 595 336x = 234Subtract 595 each side xx = 6.5Divide 36 each side $$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 $ After lunch, Marcus walked 14 miles and Anisa walked 13. In the afternoon they raised $ How much did each raise per mile? 1. Marcus: $22.00 Anisa: $ Marcus $21.00 Anisa: $ Marcus: $24.00 Anisa: $ Marcus: $20.75 Anisa: $22.75

6-3: Elimination using Addition/Subtraction  Assignment  Page 353  1 – 23, odds