SOLUTION: 2. Two numbers are such that if the square of the first number is subtracted by twice their product, the difference is -1. But twice the product added to the sum of thrice the squa

x = first number
y = second number

The square of the first number is x2

Twice their product is 2xy

So we subtract x2 from 2xy

That's 2xy - x2

So we set that difference (subtraction) equal to -1 
and that's our first equation:

2xy - x2 = -1

That's xy

that's 3x2

that's 5x

So the sum of those is 3x2 + 5x

So we add xy to that, which is 3x2 + 5x + xy 

and we set that = 10, and the second equation is

3x2 + 5x + xy = 10 

So the system of equations is

 

That has solutions:

, 

and

, 


Edwin

Let 1st number be F, and 2nd, S

Then,  ------- eq (i)

Also,  ------ eq (ii)

 ------ Subtracting eq (ii) from eq (i)

Solve the above quadratic equation to get: