Question 1146478
let x = kyle's age.
let y = kylie's age.


kyle is 2 years older than kylie, so x = y + 2.


in 2 years, the sum of their ages will be 38, so x + 2 + y + 2 = 38
combine like terms to get x + y + 4 = 38
subtract 4 from both sides of this equation to get x + y = 34


you have two equations that need to be solved simultaneously.
they are:


x = y + 2
x + y = 34


subtract y from both sides of the first equation and leave the second equation as is to get:


x - y = 2
x + y = 34


add the two equations together to get 2x = 36
solve for x to get x = 18


since x + y = 34, then y must be equal to 34 - 18 = 16


you have x = 18 and y = 16


go back to your two original equations and replace x and y with that to get:


x = y + 2 becomes 18 = 16 + 2 which is true.
x + 2 + y + 2 = 38 becomes 18 + 16 + 4 = 38 which is also true.


the values of x and y are confirmed to be good.


your solution is that kyle is 18 years old now.