6-3 Elimination Using Addition and Subtraction

- 3x + 4y = 12 3x - 6y = 18

- 3x + 4y = 12 - 3x + 4 (- 15) = 12 3x - 6y = 18 - 3x - 60 = 12 -2y/-2 = 30/-2 + 60 + 60 y = -15 -3x/-3 = 72/-3 (- 24,- 15) x = -24

4x + 2y = 28 4x - 3y = 18

4x + 2y = 28 4x + 2y = 28 (-1) 4x - 3y = 18 (-1) --> - 4x + 3y 5y/5 = 10/5 4x - 3 (2) = 18 y = 2 4x - 6 = 18 + 6 + 6 (6, 2) 4x/4 = 24/4 x = 6

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 for power tools, and earned $829. How much does the store charge per day for ladders and power tools?

let L = price of ladders per day let p = price of power tools per day 36L + 85p = 956.50 36L + 85p = 956.50 36L + 70p = 829 (-1) 36L + 70p = 829 (-1) 36L + 85p = 956.50 36L + 70 (8.5) = 829 - 36L - 70p = - 829 36L + 595 = 829 15p/15 = 127.5/15 - 595 - 595 p = 8.5 36L/36 = 234/36 L = 6.5 $6.5 per day for ladders and $8.5 per day for power tools

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.

let x = 1st number 4 (3) - 3y = 12 let y = 2nd number 12 - 3y = 12 4x - 3y = 12 - 12 - 12 2x + 3y = 6 -3y/-3 = 0/-3 6x/6 = 18/6 y = 0 x = 3 (3, 0)