Function Substitution

Introduction to function substitution:

In mathematics, function substitution system is a method used to solve system of linear equations. A system of linear equation is a position of two or three linear equations by means of two or three variables in that order.

In the direction of answer system of linear equations, we contain to solve one of those equations for an exacting variable. The explain equation is now substituted in the other equation, and the value of the other variable is obtained. In this article we are going to study how to do function substitution to solve system of linear equations.

Substitution method:

For answer the systems of equations, function Substitution is used.

In the function substitution method of solving equations, from side to side a exacting variable, another variable can be solved if any one of the equations is solved.


Steps involved in solving function Substitution method:


For answer the system of linear equations using the method of function substitution, the subsequent steps are to be followed:

Step 1: Answer anyone of the equation to write one variable in terms of other variable.

Step 2: After that Substitute this in the second equation to obtain a single variable equation.

Step 3: The after that step is to answer the single variable equation to locate the value of that variable.

Step 4: Once we obtain the value of one variable, substitute the value in some of the equation to obtain the value of the second variable.

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Solving Problems based on function Substitution:


Example 1:

Answer the subsequent system of linear equations using the method of function substitution.

x - y = -5

3x+8y = -48.
Solution:

Step 1: Rearrange the first equation,
x - y = -5
y = x + 5

Step 2:Substitute this value for y into the second equation;
3x + 8(x + 5) = -48

Step 3:Expand and simplify the equation:
3x + 8x + 40 = -48
11x = -88
x = -8

Step 4:Substitute x back into one of the original equations;
-8 - y = -5
y = -3

Solution:  x = -8, y = -3

Example 2:

Answer the subsequent system of linear equations using function Substitution method:

x + y = 25

-4x + y = 10.
Solution:

Step 1: Rearrange the first equation,
x + y = 25
y = 25 - x

Step 2:Substitute this value for y into the second equation;
- 4x + (25 - x) = 10

Step 3:Expand and simplify the equation:
-4x + 25 - x  = 10
-5x = 10 - 25
-5x = -15

x = 3

Step 4: Substitute x back into one of the original equations;
3 + y = 25
y = 22

Solution: x = 3, y = 22

These are the examples for solving substitution method.