If you add​ natalie's age and​ fred's age, the result is 43. if you add​ fred's age to 44 times​ natalie's age, the result is 88. write and solve a system of equations to find how old fred and natalie are.

Let Natalie be x, and Fred, y.
So based on 1st condition, we get
x + y =43         - Equation 1   
â´ x = 43-y - Equation 2
Now based on 2nd condition, we get
44x+y=88
Using x from Equation 2, we get
44(43-y) + y = 88
â´ 44x43 - 44y + y = 88
â´ 1892 -44y + y = 88
â´ -44y + y = 88 - 1892
â´ 43y =1804
â´ y = 1804/43
â´ y = 41.95

Using the value of y in Equation 2
x = 43 - 41.95
â´ x = 1.05

So Natalie is 1.05 yrs and Fred is 41.95 yrs old.