Henry and karyn are brother and sister. one-half of henry’s age plus twice karyn’s age equals 11. four times henry’s age minus karyn’s age equals 3. let x represent henry’s age and y represent karyn’s age. the system that can be used to find their ages is below. x + 2y = 11 4x – y = 3 find the solution to the system. what is karyn’s age?

4 years 6 months and 20 days is the age of Karyn.

Step-by-step explanation:

Let age of Henry is x years and age of Karyn be y years.

Now as per statement of the question

x + 2y = 11 (1)

and 4x - y = 3 (2)

We have to solve the equations to get the value of y or age of Karyn.

We will multiply equation 1 by 4

4x + 8y = 44(3)

Now we will subtract equation 2 from 3

(4x + 8y)-(4x - y) = 44 - 3

4x + 8y - 4x + y =41

9y = 41

y = 41/9 years ≅ 4 years and 60/9 months ≅ 4 years 6 months 20 days.