Solve the following using the substitution method and find the value of x and y:
x – 3y = 1
-3x – y = -13

The correct answer is: 4, 1

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 – 3y = 1 and -3x – y = -13
Given:
x – 3y = 1   …  (1)
-3x – y = -13…(2)
The equation (1) can be written as
x = 1 + 3y … (3)
Now, in equation (2) eliminate the variable x by substituting the value of x in terms of y from equation (3).
Hence, equation (2) becomes
-3(1 + 3y) - y  = -13
Now, apply the distributive property for the above equation,
-3 -9y -y = -13
-10y = -10
y = 1
Hence, the value of y is 1.
Now, substituting y= 1 in the equation (3), we get
x = 1 + 3(1)
x = 4
Therefore, the value of x is 4.
Hence, the solution for the system of linear equations is:
x = 4 and y= 1
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 (1) to verify the solution
    x – 3y = 1
Now, substitute x= 4 and y= 1
4 - 3(1) = 1
1 = 1
Here, L.H.S = R.H.S
Thus, the obtained solution is correct.