let

j = the age of Jane now

k = the age of Kate now

Jane is 3 times as old as Kate:

j = 3k

In 5 years Janes age will be 2 less than twice Kate's:

j + 5 = 2(k + 5) - 2

by solving the system of equations:

j = 3k

j + 5 = 2(k + 5) - 2

we find:

j = 9 years

k = 3 years

click here to see the step by step solution of the system of equations:

Jane is 9 years old now.

Kate is 3 years old now.