If you add natalie's age and fred's age, the result is 39. if you add fred's age to 3 times natalie's age, the result is 65. write and solve a system of equations to find how old fred and natalie are.

Define x and y :

Let Natalie's age be x.
Let Fred's age be y.


Construct equations:

Add​  Natalie's age and​ Fred's age, the result is 39
⇒ x + y = 39

Add​ Fred's age to 3 times​ Natalie's age, the result is 65.
⇒ y + 3x = 65


Solve x and y :

x + y = 39 (1)
y + 3x = 65  (2)


From Equation (1) :

x + y = 39
x = 39 - y


Sub x = 39 - y into equation (2) :

y + 3x = 65
y + 3(39 - y) = 65
y + 117 - 3y = 65
2y = 52
y = 26


Sub y = 26 into equation 1 :

x = 39 - 26
x = 13


Find their age :

Natalie = x = 13
Fred = y = 26


Answer : Natalie is 13 years old and Fred is 26 years old.