Solve the following using the substitution method and find the value of x and y:
x – 5y = 12
x – y = 4

The correct answer is: 2, -2

In this method, the elimination of the variable can be performed by substituting the value of another variable in an equation. Hence, this method is called the elimination by substitution method.
x – 5y = 12 and  x – y = 4
Given:
x – 5y = 12  …  (1)
x – y = 4 …(2)
The equation (2) can be written as
x = 4 + y … (3)
Now, in equation (1) eliminate the variable x by substituting the value of x in terms of y in equation (1).
Hence, equation (1) becomes
4 + y - 5y = 12
-4y = 8
y = -2
Hence, the value of y is -2.
Now, substituting y= -2 in the equation (3), we get
x = 4 + (-2)
x = 2
Therefore, the value of x is 2.
Hence, the solution for the system of linear equations is:
x = 2 and y= -2
To check whether the obtained solution is correct or not, substitute the values of x and y in any of the given equations.
Verification:
Use Equation (2) to verify the solution
 x – y = 4
Now, substitute x= 2 and y= -2
2 -  (-2) = 4
4 = 4
Here, L.H.S = R.H.S
Thus, the obtained solution is correct.