ELIMINATION METHOD STEPS

On this webpage "Elimination method steps" we are going to see how to solve linear equations in elimination method in a easy way.

Procedure for elimination method steps:

By using the below flow chart you can easily understand the elimination method steps.

Example problems of elimination method steps:

Problem 1:

Solve by elimination method

3 x + 4 y = -25

2 x - 3 y = 6

Solution:

To eliminate y,let us check the coefficients of y term

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

2 x - 3 y = 6  ---- (2)

Since the coefficients of y terms are not same,we have to find the common number for 3 and 4. The common number for 3 and 4 is 12.

To make the coefficients of y as 12,we have to multiply the first equation by 3 and the second equation by 4

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

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

Since the symbols of y terms are different,we have to add them to eliminate y

(3) + (4)            9 x + 12 y = -75

                         8 x - 12 y = 24

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

                        17 x = - 51

                             x = -51/17

                             x = -3

substitute 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

We can also verify the solution which we have found by applying these values in any of the given original equation

          3 (-3) + 4 (-4) = -25

              -9 - 16 = -25

                   - 25 = -25

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.

Problem 2:

Solve the following system of linear equations by elimination method

x + 2 y = 7

x – 2 y = 1  

Solution:

X + 2 y = 7    --------- (1)

X – 2 y = 1   --------- (2)      

For that let us consider the coefficients of x and y in both equation.

In the first equation we have + 2y and in the second equation we have -2y and the symbols are not same so we can easily eliminate the variable y by just adding two equations.

Adding (1) and (2) we get

                 X + 2 y = 7    

                X – 2 y = 1  

              -------------

                2 x = 8                           

                  x = 8/2

                  x = 4

now we have to apply the value of x in wither given equations to get the value of another variable y

Substitute x = 4 in the first equation we get

     4 + 2 y = 7

            2 y = 7 – 4

             2 y = 3

               y = 3/2       

Solution:

     x = 4

     y = 3/2    

verification:

 x  + 2 y = 7

 4 + 2(3/2)= 7

 4 + 3 = 7 

 7 = 7    


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