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

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 Option: Answer is C

Solution:
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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