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Mathematics

Find the values of x and y if :

(i) (x - 1, y + 3) = (4, 4)

(ii) (3x + 1, 2y - 7) = (9, - 9)

(iii) (5x - 3y, y - 3x) = (4, - 4)

Coordinate Geometry

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Answer

Since two ordered pairs are equal, their first components are equal and their second components are separately equal.

(i) (x - 1, y + 3) = (4, 4)

⇒ x - 1 = 4 and y + 3 = 4

⇒ x = 4 + 1 and y = 4 - 3

⇒ x = 5 and y = 1

Hence, x = 5 and y = 1.

(ii) (3x + 1, 2y - 7) = (9, - 9)

⇒ 3x + 1 = 9 and 2y - 7 = -9

⇒ 3x = 9 - 1 and 2y = -9 + 7

⇒ 3x = 8 and 2y = -2

⇒ x = 83\dfrac{8}{3} and y = -22\dfrac{2}{2}

⇒ x = 2232\dfrac{2}{3} and y = -1

Hence, x = 2232\dfrac{2}{3} and y = -1.

(iii) (5x - 3y, y - 3x) = (4, - 4)

⇒ 5x - 3y = 4 …………….(1)

And, y - 3x = - 4

⇒ y = -4 + 3x …………….(2)

Putting the value of y in (1), we get

⇒ 5x - 3(-4 + 3x) = 4

⇒ 5x + 12 - 9x = 4

⇒ 5x - 9x = 4 - 12

⇒ - 4x = - 8

⇒ x = 84\dfrac{8}{4}

⇒ x = 2

Putting the value of x in (2),

y = - 4 + 3x

⇒ y = - 4 + 3 x 2

⇒ y = - 4 + 6

⇒ y = 2

Hence, x = 2 and y = 2.

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