# Solve the following equations: i. 3 (y + 8) = 10 (y – 4) + 8 ii. x-9/x-5 = 5/7

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Solve the following equations:

i. 3 (y + 8) = 10 (y – 4) + 8

ii. $\cfrac{x-9}{x-5} =\cfrac{5}{7}$

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i. 3 (y + 8) = 10 (y – 4) + 8

∴ 3y + 24 = 10y – 40 + 8

∴ 3y + 24 = 10y – 32

∴ 3y + 24 – 24 = 10y – 32 – 24

…[Subtracting 24 from both the sides]

∴ 3y = 10y – 56

∴ 3y – 10y = 10y – 56

…[Subtracting 10y from both the sides]

∴ – 7y = – 56

∴ $\cfrac{-7y}{-7}=\cfrac{-56}{-7}$…[Dividing both the sides by – 7]

∴ y = 8

ii. $\cfrac{x-9}{x-5} =\cfrac{5}{7}$

…[Multiplying both the sides by 7 (x – 5)]

∴7 (x – 9) = 5 (x – 5)

∴7x – 63 = 5x – 25

∴7x – 63 + 63 = 5x – 25 + 63

…[Adding 63 on both the sides]

∴7x = 5x + 38

∴7x – 5x = 5x + 38 – 5x

…[Subtracting 5x from both the sides]

∴ 2x = 38

$\cfrac{2x}{2} =\cfrac{38}{2}$…[Dividing both the sides by 2]