Uncle ian spent $59 at a book store. he bought science fiction and mystery novels. the science fiction novels cost $7 apiece and the mystery novels cost $9 apiece. if uncle ian bought 7 novels, how many of each type did he buy?

2 science fiction and 5 mystery

Step-by-step explanation:

First, we will set up a system of equations.

x (science fiction) y (mystery)

x + y = 7 This is the total books bought.

7x + 9y = 59 The amount of each set to the total cost.

Now we solve.

(-7)x + y = 7 equals

-7x - 7y = -49

added to

7x + 9y = 59

this equals

2y = 10

y = 5

Now we know one. We can plug it in to find the other value.

x + 5 = 7

x = 2

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: