Tom's and tim's ages add up to 21 years. in 3 years, tom will be twice tim’s age. how old are they now?

Let X= toms age
let y = Tim's age
X+y=21
(X+3)=2(y+3)

X+3=2y+6
X-2y=3

2*(X+y=21) multiple the equation by 2
so now you have 2 equations
x-2y=3
2x+2y=3
add the equations (2y cancel out)
3x=9
solve for X and plug back into one of the original equations to get y