Solve the following using the substitution method and find the value of x and y:
- x – 4y =16
- 5x - 5y = 5

The correct answer is: 4, -5

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 - 4y = 16 and -5x- 5y = 5
Given:
-x - 4y = 16  …  (1)
-5x- 5y = 5 …(2)
The equation (2) can be written as
-x -y =1 or x + y = -1
y = -1-x … (3)
Now, in equation (1) eliminate the variable y by substituting the value of y in terms of x from equation (3).
Hence, equation (2) becomes
-x -4(-1 - x) = 16
Now, apply the distributive property for the above equation,
-x +4 +4x = 16
3x = 12
x = 4
Hence, the value of x is 4.
Now, substituting x= 4 in the equation (3), we get
y = -1-4
y = -5
Therefore, the value of y is -5.
Hence, the solution for the system of linear equations is:
x = 4 and y= -5
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-4y = 16
Now, substitute x= 4 and y= -5
-4 - 4(-5) = 16
-4 + 20= 16
16 = 16
Here, L.H.S = R.H.S
Thus, the obtained solution is correct.