Find the larger of the two numbers if their difference is 4 and the difference of squares is 104.

Let us denote the first unknown by x, and the second by y. There are two conditions in the task, which means we can make two equations. First equation: x-y = 4. And the second is x ^ 2-y ^ 2 = 104.
Having two equations, we will compose a system of equations from them.
Further, from the first equation of the system we can express one of the unknowns, let us assume y.
y = x-4. Then, in the second equation, instead of y, substitute the value just expressed (x-4). We get ^
x ^ 2- (x-4) ^ 2 = 104. We expand the brackets by squaring the expression in them.
x ^ 2- (x ^ 2-8x + 16) = 104
Expand the brackets: x ^ 2-x ^ 2 + 8x-16 = 104. The x squared cancels out and we get the usual linear equation.
8x-16 = 104
8x = 104 + 16
8x = 120
x = 120/8
x = 15
Substituting x = 15 into the original equation and we get y = 15 – 4 = 11.
Answer: The larger of the numbers is the first (x = 15, y = 11).