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PAIRS OF EQUATIONS

PAIRS OF EQUATIONS. Consider the following information!. Two coffees & three doughnuts cost 290p. Three coffees & one doughnut cost 260p. How much is each item?. Coffee = 70p & doughnut = 50p !!. Check. DON’T COPY !!. 2c + 3d =. 140 + 150 = 290. 3c + d =. 210 + 50 = 260.

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PAIRS OF EQUATIONS

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  1. PAIRS OF EQUATIONS

  2. Consider the following information! Two coffees & three doughnuts cost 290p. Three coffees & one doughnut cost 260p. How much is each item? Coffee = 70p & doughnut = 50p !! Check DON’T COPY !! 2c + 3d = 140 + 150 = 290. 3c + d = 210 + 50 = 260.

  3. Combining Equations Suppose a banana costs 20p and a kiwi costs 30p. Using b and k as shorthand. 5b + 3k = 190 3b + 2k = 120 ADDING SUBTRACTING MULTIPLYING 5b + 3k = 190 5b + 3k = 190 3b + 2k = 120 3b + 2k = 120 X5 3b + 2k = 120 15b + 10k = 600 8b + 5k = 310 2b + k = 70

  4. Eliminating a Letter Ex1 Ex2 3a + b = 13 x + y = 13 a + b = 7 x - y = 5 2a = 6 2x = 18 Subtract  add a = 3 x = 9 use 2nd equation use top equation 9 + y = 13 3 + b = 7 b = 4 y = 4 Also 3x3 + 4 = 13 Also 9 – 4 = 5 Note: y and –y cancel by adding Note: b and b cancel by subtracting

  5. Ex3 Ex4 3p + q = 3 c + 2d = 1 3p + 4q = 21 3c – 2d = 19 3q = 18 4c = 20 Subtract  add q = 6 c = 5 use top equation use top equation 5 + 2d = 1 3p + 6 = 3 2d = -4 3p = -3 d = -2 p = -1 Also 3x5 – 2x(-2) Also 3x(-1) + 4x6 = -3 + 24 = 21 = 15 – (-4) = 19 Note: 2d and –2d cancel by adding Note: 3p and 3p cancel by subtracting

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