|

Elimination by Addition or Subtraction Method Independent Simultaneous Equations

Simultaneous System of Equations

If there is only one solution for each unknown that satisfies both equations, the two equations of the system are called Independent Simultaneous Equations in two variables.

Steps for Solving Independent Simultaneous Equations

Simultaneous equations involving two unknown quantities are solved by using following steps:

Step-I: Eliminate one of the unknowns
Step-II: Solve for the other unknown
Step-III: Find the value of the unknown previously eliminated

Method of Solving Independent Linear  Equations Simultaneously

There are following common methods of solving independent linear equations simultaneously.

  1. Elimination by addition or subtraction
  2. Elimination by substitution
  3. Elimination by comparison
  4. Use of graphs
  5. Use of matrix algebra

Elimination by Addition or Subtraction Method Independent Simultaneous Linear Equations

Elimination by Addition or Subtraction

These is another method of solving systems of equations called the Addition or Subtraction method. Like the Substitution Method and Comparison Method it produces exact solutions and can used on any system of two linear equations involving two variables.

To solve a system of two equations in two variables by addition or subtraction, following are the steps.

  1. If necessary, multiply one or both equations by a non zero number that will make the coefficients of one of the variables identical, except perhaps for signs.
  2. Add or subtract the equations to eliminate one of the variables.
  3. Solve for the variable in the resulting equation.
  4. Substitute the solution into one of the original equations and solve for the remaining variable.
  5. Check the solution in both original equations.

We consider the following examples to illustrate the use of the Addition and Subtraction Method.

Elimination by Addition

Question:-    5x + 2y = 33 and 10x – 4y = 54

Solution:-

Given Set of equations:

 5x + 2y = 33              ………(i)
10x – 4y = 54             ………(ii)

Step-I: We eliminate “y” by multiplying equation (i) by 2 and adding it in equation (ii). We get

Example of Elimination by Addition Independent Linear Equations Simultaneously

Step-II: Solve for x

            X =  = 6

Step-III: For y, Putting x = 6 in equation (ii), we get

10(6) – 4y = 54
60 – 4y = 54
– 4y = 54 – 60
– 4y = – 6     (Cancellation of ‘-‘ from both side)
y =

y =

Thus the solution set of the given system of equations is

S.S = {(x, y)} = {(6, )}

To Check: Substitute x = 6 and y =   in both of the original equations

5x + 2y = 33              ………(i)
5(6) + 2 = 33
30 + 3 = 33
33 = 33 (a true statement)

10x – 4y = 54             ………(ii)
10(6) – 4 = 54
60 – 6 = 54
54 = 54 (a true statement)

Elimination by Subtraction

Questions:-   4x – 2y = 50 and 5x – y = 10

Solution:-

Given Set of equations:

4x – 2y = 50              ………(i)
5x – y = 10               ………(ii)

Step-I: We eliminate “y” by multiplying equation (ii) by 2 and subtracting it in equation (i). We get

Example of Elimination by Subtraction Independent Linear Equations Simultaneously

Step-II: Solve for x

            X =  = –5

Step-III: For y, Putting x = –5  in equation (i), we get

4(–5) – 2y = 50
–20 – 2y = 50
– 2y = 54 + 20
– 2y = 74

y =

y = –35

Thus the solution set of the given system of equations is

S.S = {(x, y)} = {(-5, -35)}

To Check: Substitute x = -5 and y = -35 in both of the original equations

4x – 2y = 50              ………(i)
4(-5) – 2(-35) = 50
-20 + 70 = 50
50 = 50 (a true statement)

5x – y = 10               ………(ii)
5(-5) – 1(-35) = 10
-25 + 35 = 10
10 = 10 (a true statement)

Similar Posts