You can set it up as follows:
Tess (T) + Audrey (A) + Sam (S) = 38
T = A + 2
S = 3A - 29
You need to be able to solve for one variable at a time. As we can already see everything expressed in terms of A, let's start there. We will plug in for T and S in terms of A to our original equation.
(A + 2) + A + (3A - 29) = 38, which simplifies to:
5A - 27 = 38
5A = 65
A = 13
Now we know Audrey is 13 years old. To get the remaining ages, go back to our secondary equations, and plug in A.
T = A + 2, or T = 13 + 2; T = 15
So Tess is 15 years old.
Now we have two different equations to choose from to get the remaining age, Sam's. Let's use the easiest equation, T + A + S = 38.
So, 15 + 13 + S = 38
This tells us S = 10
So, we know Sam is 10 years old, Audrey is 13 years old, and Tess is 15 years old.
Hope that helps!!