System of Equations. Gary has 4 boxes of fruit and 2 pounds of pineapple. Susie has 3 boxes of fruit and 3 pounds of pineapple. What would the weight.

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Presentation transcript:

System of Equations

Gary has 4 boxes of fruit and 2 pounds of pineapple. Susie has 3 boxes of fruit and 3 pounds of pineapple. What would the weight be of each box of fruit if both Gary and Susie had the same total weight of fruit? Define our variablesy: total weight x: boxes of fruit

Gary has 4 boxes of fruit and 2 pounds of pineapple. Susie has 3 boxes of fruit and 3 pounds of pineapple. What would the weight be of each box of fruit if both Gary and Susie had the same total weight of fruit? Gary’s total = Susie’s total 4x + 2 = 3x + 3 Gary y=4x+2 Susie y=3x+3

Let’s solve for x 4x + 2 = 3x + 3

Both Gary and Susie have 6 pounds Gary y=4x+2Susie y=3x+3 Substitute x = 1 and solve for the total.

Solve this system: y=4x+2y=3x+3

y = 2x + 9 y = 5x – 3 x= 4, y = 17 (4, 17) y = 7x – 15 y = 3x + 5 x = 5, y = 20 (5, 20) click here for answer 1.2. click here for answer

y=–5x+14x–y=10 x – (–5x + 14) = 10

y = 2x – 1 5x – 2y = 4 x= 2, y = 3 (2, 3) x = –y x – 3y = 15 x = 9, y = 1 (9, 1) click here for answer 3.4.

y = x y = 2x + 1 x= –1, y = –1 (–1, –1) y = x + 7 x + y = 35 x = 14, y = 21 (14, 21) click here for answer 5.6.

y = 3x x + 2y = –21 x = –3, y = –9 (–3, –9) y = 3x – 8 y = 4 – x x = 3, y = 1 (3, 1) click here for answer 7.8.