The difference between the square of two numbers is five. twice the square of the second number is subtracted from three times the square of the first number is 19. find the numbers. show work. the difference between the square of two numbers is five. twice the square of the second number is subtracted from three times the square of the first number is 19. find the numbers. show work.

Let us assume the first number to be = x
Let us assume the second number to be = y
Then
x^2 - y^2 = 5
x^2 = y^2 + 5
And
3x^2 - 2y^2 = 19
Multiplying the first equation by -2, we get
- 2x^2 + 2y^2 = - 10
Now subtracting the two equations, we get
x^2 = 9
x = 3
Putting the value of "x" in the first equation, we get
(3)^2 - y^2 = 5
9 - y^2 = 5
y^2 = 4
y = 2

I hope that the procedure is clear enough for you to understand and this is the answer that you were looking for.