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X+8Y=19 AND 5X+11Y=28

Answer»

x + 8y = 19 - (1) \\ 5x + 11y = 28 - (2) \\ \\ (1) * 11 = 11x + 88y = 209 - (3) \\ (2) * 8 = 40x + 88y = 224 - (4) \\ \\ (4) - (3) \\ = (40x + 88y) - (11x + 88y) = 224 - 209 \\ = 40x + 88y - 11x - 88y = 15 \\ = 40x - 11x = 29x = 15 \\ \\ x = \frac{15}{29}


x + 8y = 19 \\ \\ = \frac{15}{29} + 8y = 19 \\ \\ 8y = 19 - \frac{15}{29} = \frac{551 - 15}{29} = \frac{536}{29} \\ \\ y = \frac{536}{29} / 8 = \frac{536}{29} * \frac{1}{8} = \frac{536}{232} = \frac{67}{29} \\ \\ \therefore x = \frac{15}{29}; y = \frac{67}{29}


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