Question

If x + y = 7 and x – y = 2, find the value of xy.

Answer 1

Given equations: x + y = 7 and x – y = 2

Step-wise calculation:

1. From these two equations, add them:

(x + y) + (x – y) = 7 + 2

⇒ 2x = 9

⇒ x = `9/2`

⇒ x = 4.5

2. Substitute the value of (x) in the first equation:

4.5 + y = 7

⇒ y = 7 – 4.5

⇒ y = 2.5

⇒ y = `5/2`

3. Calculate (xy):

`xy = 9/2 xx 5/2`

`xy = 45/4` 

xy = 11.25

So the value of (xy) in fraction form is `45/4`.