Solve the following using the substitution method and find the value of x and y:
x + 4y = -18
2x + y = -1

The correct answer is: 2, -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 = -18 and 2x + y = -1 
Given:
x + 4y = -18 …  (1)
2x + y = -1  …(2)
The equation (1) can be written as
x = -18 -4y … (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
2(-18 -4y) +y = -1
Now, apply the distributive property for the above equation,
-36 -8y + y= -1
-36 -7y = -1
-7y = 35
y = -5
y = -5
Hence, the value of y is -5.
Now, substituting y = -5 in the equation (3), we get
x = -18 -4(-5)
x =-18+ 20
x = 2
Therefore, the value of x is 2.
Hence, the solution for the system of linear equations is:
x = 2 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 (2) to verify the solution
2x + y = -1 
Now, substitute x= 2 and y= -5
2(2) + (-5) = -1
4 - 5= -1
-1 = -1
Here, L.H.S = R.H.S
Thus, the obtained solution is correct.