At present, Shyam is twice as old as his sister. Three years back, he was thrice her age. Find his?

Let's call them B for boy and G for girl.

Given:
B = 2G
(B - 3) = 3(G - 3)

You have two lines. Where they cross, the values of x and y satisfy both equations simultaneously, so it is called a simultaneous system. There are two ways to find that point. Substitution is when you solve one equation for one variable and substitute that into the other equation. Since the first equation is already solved, just sub 2G for B in the second equation.

(2G - 3) = 3(G - 3) Evaluate.
2G - 3 = 3G - 9
6 = G The girl is 6 years old and the boy is 12 years old.

Elimination is when you add the equations in a way to eliminate one variable. Otherwise the process is the same.

B = 2G
(B - 3) = 3(G - 3)

B - 3 = 3G - 9
B .... = 2G
-------------- SUBTRACT
-3 = G - 9

6 = G <-- SAME ANSWER