Match each word problem to the equation that models it. tiles the sum of the squares of two positive integers is 394. if one integer is 2 less than the other and the larger integer is x, find the integers.

Let
x--------> the larger integer
y-------> the smaller integer

we know that
x²+y²=394-----> equation 1
x=y+2-----> equation 2
substitute equation 2 in equation 1
[y+2]²+y²=394-----> y²+4y+4+y²=394
2y²+4y-390=0

using a graph tool----> to resolve the second order equation
see the attached figure

the solution is
y=13
x=y+2---> x=13+2---> x=15

the answer is
the numbers are 15 and 13