Solve the following using the substitution method and find the value of x and y:
5x + y = -10
2x + 5y = 19

The correct answer is: -3, 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.
5x+ y = -10 and 2x+ 5y = 19
Given:
5x+y = -10  …  (1)
2x+5y = 19 …(2)
The equation (1) can be written as
y = -10-5x … (3)
Now, in equation (2) eliminate the variable y by substituting the value of y in terms of x in equation (3).
Hence, equation (2) becomes
2x +5(-10 - 5x) = 19
Now, apply the distributive property for the above equation,
2x -50 -25x = 19
-23x = 69
x = -3
Hence, the value of x is -3.
Now, substituting x= -3 in the equation (3), we get
y = -10-5(-3)
y =-10+ 15
y = 5
Therefore, the value of y is 5.
Hence, the solution for the system of linear equations is:
x = -3 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+5y = 19
Now, substitute x= -3 and y=5
2(-3) + 5(5) = 19
-6 + 25= 19
19 = 19
Here, L.H.S = R.H.S
Thus, the obtained solution is correct.