Find the value of x and y in the simultaneous equation: 3x + y =…

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: Option C
Explanation

3x + y = 21 … (i);

xy = 30 … (ii)

From (ii), (y = frac{30}{x}). Putting the value of y in (i), we have

3x + (frac{30}{x}) = 21

(implies) 3x(^2) + 30 = 21x

3x(^2) – 21x + 30 = 0

3x(^2) – 15x – 6x + 30 = 0

3x(x – 5) – 6(x – 5) = 0

(3x – 6)(x – 5) = 0

3x – 6 = 0 (implies) x = 2.

x – 5 = 0 (implies) x = 5.

If x = 2, y = (frac{30}{2}) = 15;

If x = 5, y = (frac{30}{5}) = 6.

There is an explanation video available below.

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