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

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Question 1058629: 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 square of the first number and five times that number gives 10.
Found 2 solutions by Edwin McCravy, MathTherapy:
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
2. Two numbers 
x = first number
y = second number

are such that if the square of the first number 
The square of the first number is x2

is subtracted from twice their product, 
Twice their product is 2xy

So we subtract x2 from 2xy

That's 2xy - x2

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

2xy - x2 = -1

But twice the product 
That's xy

added to the sum of thrice the square of the first number 
that's 3x2

and five times that number 
that's 5x

So the sum of those is 3x2 + 5x

gives 10
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
Answer by MathTherapy(10553)   (Show Source): You can put this solution on YOUR website!

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 square of the first number and five times that number gives 10.
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:  

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