Solving Linear Equations Substitution Method

Introduction :

The linear equations for the substitution methods are one of the methods in the systems of equations in the algebra section. The substitution methods are nothing but the variable can be found by using the equations and the value of one variable can be determined. Then, other variable can be found by substituting the variable value in another equation. Now we see the solving of linear equations by substitution method.

About Solving of Linear Equations by Substitution Method:

Now we are going to see the steps for solving the linear equations by substitution methods are as follows,

The equation should be choose and place one variable in one side and the other variables and values on the other side.

Then, in the second step these equations should be substituted in one equation and the value can be determined.

The other value of the variable can be determined by substituting the value in another equation.

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Problems for Solving the Equations by Substitution Method:

Example 1:

Solve the given two equations by substitution method:

x + y = 2

y + 10 = 2x

Solution:

Choose one of the equations for solving the linear systems as follows,

x + y = 2

x = 2 – y

Now put the value of x in the equation y + 10 = 2x

y + 10 = 2x

y + 10 = 2(2 – y)

y + 10 = 4 – 2y

y + 2y = 4 - 10

3y = -6

y = -2.

Put the value of y in the equation x = 2 - y

x = 2 - y

x = 2 - (-2)

x = 2 + 2

x = 4

The values are x = 4 and y = -2.

Example 2:

The given two equations for solving linear system are:

x + y = 4

y + 8 = x

Solution:

Choose one of the equations for solving the linear systems as follows,

x + y = 4

x = 4 - y

Now put the value of x in the equation y + 8 = x

y + 8 = x

y + 8 = 4 - y

y + y = 4 - 8

2y = - 4

y = -2.

Put the value of y in the equation x = 4 - y

x = 4 - y

x = 4 - (-2)

x = 4 + 2

x = 6

The values are x = 6 and y = -2.