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

### Question

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

### Options

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

### 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.

## Dicussion (1)

• 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.