Question

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. Please 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. Please show work. @Mathematics

Answer 1

"The difference between the square of two numbers is five. "
means:

x^2-y^2=5

"Twice the square of the second number is subtracted from three times the square of the first number is 19"
means:

3x^2-2y^2=19

x^2-y^2=5 (1)
3x^2-2y^2=19 (2)

multiply (1) by -2 and add it to (2)

x^2=9
x={3,-3}
y=sqrt(9-5)=sqrt4={2,-2}

x={3,-3}
y={2,-2}

Answer 2

Quick question, would all four numbers work in the problem?

Answer 3

And would I leave it like that or another way?
x={3,-3}
y={2,-2}

Answer 4

Yes, all four answers are equally important because it is quadratic, and so the two graphs intercept at two points. Convention is to write the answers in the brackets from lowest to highest, but it's not technically wrong to do it in a different order.