Study Substitution

Introduction to Substitution:-

In the substitution of solve equation, through a particular variable, another variable can be solve if any one equation is solve. A linear equation is the grouping of the variables, even and operators, which represent a straight line. For example x+y = three Here x and y are variables. Three is the constant +, = are operators. For study the system of equations, Substitution method is used. There are three methods to study substitution a system of linear equations Substitution method, Elimination Method, Graphical method. In this article let us see study substitution method. Please express your views of this topic solving systems of equations by substitution answers by commenting on blog.


Steps involved in study Substitution:-


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

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

Step 2: Then Substitute this in the next equation to get a single variable equation.

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

Step 4: Once we get the rate of one variable, substitute the rate in any of the equation to get the rate of the subsequent variable.

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Example problems for study substitution:-


Example 1:-

Study the following system of linear equations using the method of substitution.

x - y = -5

3x+8y = -48

Solution:-

Rearrange the first equation,

x - y = -5

y = x + 5

Substitute this value for y into the second equation;

3x + 8(x + 5) = -48

Expand and simplify the equation:

3x + 8x + 40 = -48

11x = -88

x = -8

Substitute x back into one of the original equations;

-8 - y = -5

y = -3

Solution:-

x = -8, y = -3

Example 2:-

Study the following system of linear equations using Substitution method:.

x + y = 25

-4x + y = 10.

Solution:-

Rearrange the first equation,

x + y = 25

y = 25 - x

Substitute this value for y into the second equation;

- 4x + (25 - x) = 10

Expand and simplify the equation:

-4x + 25 - x = 10

-5x = 10 - 25

-5x = -15

x = 3

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.