Answer:
Explanation:
Let x be the larger number.
Let y be the smaller number.
x - y = 5
x^2 - y^2 = 65 Factor the left.
(x - y)(x + y) = 65 Substitute the first equation into this equation.
5 *(x + y) = 65 Divide both sides by 5
x + y = 65/5
x + y = 13
Now list the two binomials one after the other.
x + y = 13
x - y = 5 Add
2x = 18 Divide by 2
2x/2 = 18/2
x = 9
x + y = 13 Substitute 9 for x
9 + y = 13 Subtract 9 from both sides.
y = 13 - 9
y = 4
Answer