Question

x/6 + y/16 = 6; y/12 - x/9 = 2 find the value of x and y. (ans: x= 18 y = 48)​

Answer 1

Answer:

here is your answer hope it helps

Answer 2

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$\frac{x}{6} + \frac{y}{16} = 6 \: \: \: ..............(i)\\ \\ \frac{y}{12} - \frac{x}{9} = 2 \: \: \: ..............(ii)$

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firstly consider equation (i)

$\frac{x}{6} + \frac{y}{16} = 6 \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \: \: \frac{8x + 3y}{48} = 6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \: 8x + 3y = 6 \times 48 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \implies \: 8x + 3y = 288 \: \: ...........(iii)$

now, consider equation (ii)

$\frac{y}{12} - \frac{x}{9} = 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \: \frac{3y - 4x}{36} = 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \: 3y - 4x = 2 \times 36 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \implies \: 3y - 4x = 72 \: ..............(iv)$

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now, we have two equations;

8x+3y = 288 ..............(iii)

3y-4x = 72 ................(iv)

solve these equations by elimination method;

subtract equation (iv) from equation (iii)

→ 8x + 3y - (3y - 4x) = 288 - 72

→ 8x + 3y - 3y + 4x = 288 - 72

→ 8x + 4x = 216

→ 12x = 216

→ x = 216/12

→ x = 18

now substitute the value of x in equation (iv)

→ 3y - 4x = 72

→ 3y - 4(18) = 72

→ 3y - 72 = 72

→ 3y = 72 + 72

→ 3y = 144

→ y = 144/3

→ y = 48

hence, value of x is 18 and y is 48