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Properties of Modulus

Solve the fol...

Question

Solve the following equations:
$10 x + y + z = 12$ ,
$2 x + 10 y + z = 13$ ,
$2 x + 2 y + 10 z = 14$

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Solution

$10 x + y + z = 12 \dots (1) 2 x + 10 y + z = 13 \dots (2) 2 x + 2 y + 10 z = 14 \dots (3) (1) - (2) 8 x - 9 y = - 1 8 x = 9 y - 1 x = \frac{9 y - 1}{8} \dots (4) (2) - (3) 8 y - 9 z = - 1 9 z = 1 + 8 y z = \frac{1 + 8 y}{9} \dots (5) ⟹ 10 (\frac{9 y - 1}{8}) + y + (\frac{1 + 8 y}{9}) = 12 405 y - 45 + 36 y + 4 + 32 y = 432 473 y = 473 y = 1 ⟹ x = \frac{9 (1) - 1}{8} = 1 ⟹ z = \frac{1 + 8 (1)}{9} = 1$

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