Question

Find x and y, if `[(3x, 8)][(1, 4),(3, 7)] - 3[(2, -7)] = 5[(3, 2y)]`

Answer 1

`[(3x, 8)][(1, 4),(3, 7)] - 3[(2, -7)] = 5[(3, 2y)]`

`=> [(3x + 24, 12x + 56)] - [(6, -21)] = [(15, 10y)]`

`=> [(3x + 24 - 6, 12x + 56 + 21)] = [(15, 10y)]`

`=> [(3x + 18, 12x + 77)] = [(15, 10y)]`

Comparing the corresponding elements, we get

∴ 3x + 18 = 15

`=>` 3x = 15 – 18 = –3

∴ x = `(-3)/3` = –1

And 12x + 77 = 10y

`=>` 12 × (–1) + 77

`=>` 10y = –12 + 77

`=>` 10y = 65

∴ y = `65/10` = 6.5

Hence x = –1, y = 6.5