**Answer:**

**Step-by-step explanation:**

So the first step is to simply set up the problem based on what we are given. So here have two numbers, we are going to call the first number x and the second one y. With that now addressed, we can now proceed with the setup.

So the difference between the squares of the numbers is 24. So we have:

Then it says that three times the square of the first number (which we said was x) increased by the square of the second number is 76. So:

Now we can see that this is simply a system of equations and we can use elimination to solve this! We even have the setup already as the coefficients in front of our y are opposite in sign and are equal. So:

We can cancel our y squared terms out and that leaves, when we add the equations together:

We can then solve for x by diving by four and taking the square root of the result.

Therefore, x = ±5

We have both negative and positive answers because if we squared -5 or +5 they would both give us 25. So we cant rule a negative answer out yet.

So now we can plug in x = -5 or +5 to either equation to solve for y as so:

So y = ±1

In this case both negative and positive versions of our answer work (you can also double check), so we are left with:

x = ±5 and y = ±1