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.

Step-by-step explanation:

The antiderivative of the function is the same as the integral. To find the integral or antiderivative, reverse the process of differentiation method on each term.

Currently the function 1/5 has degree 0. Through integration we increase the degree of each term by 1 and divide by the degree. So 1/5 becomes 1/5 x. But the degree of x is 1 so dividing by 1 only gives the same term.For terms where x is in the denominator, we recognize it as a natural log function and write as ln x. Since -3/x is the original then it becomes - 3 ln x.

Thus 1/5 - 3/x becomes . We add a constant C for any possible constant that was eliminated during differentiation.