passpadi

2019

Mathematics

JAMB

Find the value of x and y in the simultaneous equation: 3x + y = 21; xy = 30

A.

x = 3 or 7, y = 12 or 8

B.

x = 6 or 1, y = 11 or 5

C.

x = 2 or 5, y = 15 or 6

D.

x = 1 or 5, y = 10 or 7

Correct Answer: x = 2 or 5, y = 15 or 6

Explanation

3x + y = 21 ... (i); xy = 30 ... (ii) From (ii), y = 30/x . Putting the value of y in (i), we have 3x + 30/x = 21 ⟹ 3x2 + 30 = 21x 3x2 - 21x + 30 = 0 3x2 - 15x -6x + 30 = 0 3x(x - 5) - 6(x - 5) = 0 (3x - 6)(x - 5) = 0 3x - 6 = 0 ⟹ x = 2. x - 5 = 0 ⟹ x = 5. If x = 2, y = 30/2 = 15; If x = 5, y = 30/5 = 6.

3x + y = 21 ... (i); xy = 30 ... (ii) From (ii), y = 30/x . Putting the value of y in (i), we have 3x + 30/x = 21 ⟹ 3x2 + 30 = 21x 3x2 - 21x + 30 = 0 3x2 - 15x -6x + 30 = 0 3x(x - 5) - 6(x - 5) = 0 (3x - 6)(x - 5) = 0 3x - 6 = 0 ⟹ x = 2. x - 5 = 0 ⟹ x = 5. If x = 2, y = 30/2 = 15; If x = 5, y = 30/5 = 6.
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