ELIMINATION METHOD

Elimination method :

Here we are going to see how to solve any linear equation by using this method.

Steps in Elimination Method

In the given linear equations we can eliminate any one of the variables.

The flow chart given below represents, what are the steps to be done in this method.

Elimination method - Examples

Let us consider the example below to understand this topic better

Question 1 :

Solve by elimination method

3 x + 4 y = -25

2 x - 3 y = 6

Solution :

3 x + 4 y = -25 ---- (1)

2 x - 3 y = 6  ---- (2)

Since the coefficients are different, we have to find the common number for 4 and 3.The common number for 4 and 3 is 12.

(1) x 3 => 9 x + 12 y = -75

(2) x 4 => 8 x - 12 y = 24

Since the signs are different, we have to add equation for eliminating y.

(1) + (2)         9 x + 12 y  =  -75

                       8 x - 12 y  =  24

                       -------------------

                        17 x  =  - 51

                             x  =  -51/17

                             x  =  -3

Apply x  =  -3 in the first equation

 3 (-3) + 4 y  =  -25

- 9 + 4 y  =  -25 

4 y  =  -25 + 9

4 y  =  -16

y  =  -16/4

y  =  -4

Solution :

      x = -3

      y = -4

By applying the solution in the given equation, we may verify the solution.

3 (-3) + 4 (-4) = -25

 -9 - 16 = -25

- 25 = -25

So, we can decide the answer what we got is correct.

Question 2 :

Solve by elimination method

2 x + 3 y = 5

3 x + 4 y = 7

Solution :

2 x + 3 y = 5  ---- (1)

3 x + 4 y = 7  ---- (2)

The coefficients of x and y are different.Since the symbols of x terms and y terms are same, we can eliminate either x or y term.

So, we are going to eliminate "y" for that we have to find the L.C.M for 3 and 4.The L.C.M for 3 and 4 is 12.

(1) x 4 => 8 x + 12 y = 20

(2) x 3 => 9 x + 12 y = 21

Since the signs are same we have to subtract the 2^nd equation from 1^st equation equation for eliminating y.

(1) - (2)          8 x + 12 y = 20

                      9 x + 12 y = 21

                      (-)    (-)      (-)

                    -------------------

                        -1 x = - 1

                             x = -1/(-1)

                             x = 1

Substitute x = 1 in the first equation

8 (1) + 12 y = 20

8 + 12 y = 20 

12 y = 20 - 8

12 y = 12

 y = 12/12

y = 1

Solution :

      x = 1

      y = 1

By applying the solution in the given equation, we may verify the solution.

          8 x + 12 y = 20

          8(1) + 12 (1) = 20

                 20 = 20

So we can decide the answer what we got is correct.

Elimination method worksheet contains some practice questions based on this topic.You can also try that.

Related topics

• Solve by graphing method
• Solve by substitution
  
• Synthetic Division
• Rational Expressions
• Rational Zeros Theorem
• LCM -Least Common Multiple
• GCF-Greatest Common Factor
• Simplifying Rational Expressions
• Factoring Polynomials
• Factoring a Quadratic Equation
• Factoring Worksheets
• Framing Quadratic Equation From Roots
• Framing Quadratic Equation Worksheet
• Remainder Theorem
• Relationship Between Coefficients androots
• Roots of Cubic equation
• Roots of Polynomial of Degree4
• Roots of Polynomial of Degree5

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