Find two numbers if the second number equals 4 less than the square of the first number and their sum is 38.

We can set up a system of equations like this, where x is the first number and y is the second:



Since we know what y is equal to, we can plug that into the second equation for y to solve for x:



x can equal either 36 or 49.  If x equals 36:



If x equals 49:



Although both are solutions, x=36 and y=2 or x=49 and y=-11, I would use x=36 and y=2 because plugging the 49 and -11 in causes a predicament:



*Note that the negative solution of √49 does work

Plugging in 36 and 2 turns out fine: