# Substitution method

Substitution Method:

Follow steps given below to understand Substitution Method:

Step 1: Find the value of one variable, say y in terms of the other variable, i.e., x from either equation, whichever is convenient.

Step 2: Substitute this value of y in the other equation, and reduce it to an equation in one variable, i.e., in terms of x, which can be solved. Sometime, one can get statements with no variable. If this statement is true, you can conclude that the pair of linear equations has infinitely many solutions. If the statement is false, then the pair of linear equations is inconsistent.

Step 3: Substitute the value of x (or y) obtained in Step 2 in the equation used in Step 1 to obtain the value of the other variable.

For Example: Solve the following pair of equations by substitution method: 7x – 15y = 2 and x + 2y = 3

We can re-write x + 2y = 3 as x = 3 – 2y – (1)

Substituting value of x in 7x – 15y = 2, we get,

7(3 – 2y) – 15y = 2

21 – 14y – 15y = 2

-29y = -19

Thus, y = 19/29.

Now, substituting value of y in (1), we get,

x = 3 – 2(19/29) = 49/29.