Question

If (x, y) is a solution of the system of equations above and x > 0, what is the value of xy ?

- 1
- 2
- 3
- 9

## The correct answer is: 1

### Solution:-

- We have given two equations

y = x^{2} ------- (1)

and 2y + 6 = 2 (x+3) ------- (2)

- Substituting value of y from equation (1) in equation (2) we get,

2(x^{2}) + 6 = 2 (x + 3)

- Further solving the equation we get,

2x^{2} + 6 = 2x + 6

- As, there is term 6 on both sides we will subtract 6 from both sides. So subtracting 6 from both sides of equation we get,

2x^{2} = 2x

- Dividing both sides of equation by 2 we get,

x^{2 }= x

- Dividing both sides of equation by x we get,

x = 1

- As x = 1 , we will put this value in equation (1), we get

y = (1)^{2}

y = 1

- So, the value of xy will be,

xy = 1×1

xy = 1

- Therefore, the correct option is (A) 1

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