Solve the following using the substitution method and find the value of x and y:
-x + 2y = 9
-5x – 4y = -11

The correct answer is: -1, 4

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 + 2y = 9 and       -5x – 4y = -11
Given:
-x + 2y = 9   …  (1)
-5x – 4y = -11 …(2)
The equation (1) can be written as
x = -9 + 2y … (3)
Now, in equation (2) eliminate the variable x by substituting the value of x in terms of from in equation (3).
Hence, equation (2) becomes
-5(-9 + 2y) -4y = -11
Now, apply the distributive property for the above equation,
45 -10y -4y = -11
-14y = -11 -45
-14y = -56
y = 4
Hence, the value of y is 4.
Now, substituting y= 4 in the equation (3), we get
x = -9 + 2(4)
x = -1
Therefore, the value of x is -1.
Hence, the solution for the system of linear equations is:
x = -1 and y= 4
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 + 2y = 9
Now, substitute x= -1 and y= 4
-(-1) + 2(4) = 9
1 + 8= 9
9 = 9
Here, L.H.S = R.H.S
Thus, the obtained solution is correct.