Exercise 34 Page 248

To begin we will create two equations. One to represent the age of the dog (in dog years), and one to represent the age of the cat (in cat years).

• Dog: It is given that the current age of the dog in dog years is $16.$ For every human year the dog ages $7$ dog years. If we let $x$ represent the number of human years that have passed and $y$ represents the age of the dog, we can write the following equation for the dog's age in dog years.

• Cat: It is given that the current age of the cat in cat years is $28.$ For every human year the cat ages $4$ cat years. Since $x$ represents the number of human years that have passed and $y$ represents the age of the cat, we can write the following equation for the cat's age in cat years.

To find the number of human years it will take for the animals to reach the same age in their respective years we must find the value of $x$ that makes the equations equal the same $y\text{-}$value. We can determine this graphically.

From the graph we can see that the lines intersect at $(4,44).$ This means that after $4$ more human years both animals will be $44$ years old in their respective years.