Solve the following using the substitution method and find the value of x and y:
-2x - 2y = -14
-5x – y = -23

The correct answer is: 4, 3

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.
-2x- 2y = -14 and -5x- y = -23
Given:
-2x- 2y = -14  …  (1)
-5x- y = -23…(2)
The equation (1) can be written as
x + y = 7
y = 7- x … (3)
Now, in equation (2) eliminate the variable y by substituting the value of y in terms of x from equation (3).
Hence, equation (2) becomes
-5x - (7 - x) = -23
-5x -7 +x = -23
-4x -7 = -23
-4x = -16
x = 4
Hence, the value of x is 4.
Now, substituting x= 4 in the equation (3), we get
y = 7 - 4
y = 3
Therefore, the value of y is 3.
Hence, the solution for the system of linear equations is:
x = 4 and y=3
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
-5x – y = -23
Now, substitute x= 4 and y=3
-5(4) -(3) = -23
-20 -3 = -23
-23 = -23
Here, L.H.S = R.H.S
Thus, the obtained solution is correct.