scoooby doooo

$x+y=8=4(x-y)\Rightarrow \frac{x+y}{2}=4, \frac{x-y}{2}=1 \Rightarrow (\frac{x}{2})^2+\frac{xy}{2}+(\frac{y}{2})^2=16, (\frac{x}{2})^2-\frac{xy}{2}+(\frac{y}{2})^2=1$ . Subtract the two equations to get $xy=16-1=15$ .

It says sum of two numbers = 8 So, $x + y = 8\cdot\cdot\cdot(1)$ Their sum is 4 times their difference. So, $\frac{8}{4} = 2$ So, $x - y = 2\cdot\cdot\cdot(2)$ Hence by elimination, we get, $2x = 10$ $x = 5$ putting in eq. (1), we get $5 + y = 8$ $= y = 8-5$ $= y = 3$ Hence their product is, $5 × 3 = 15$ Hence Proved