Linear Equations with two variable(3)

the method of elimination""

Example 1:  Solve the following equations

  x+ y = 5 , 2x –3 y = 10

the answer :

  x  +  y  = 5 ………. ×3

2x – 3y = 10 ………..×1

3 x  + 3 y = 15

2 x – 3 y = 10      add

5 x = 25

X=25 /5 

X =5

 Put value of x  in the first equation to get value of y

x+ y= 5

5 + y = 5

Y =5 – 5

Y = 0

the solution to this equations = {(5 , 0)}

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Example 2:Solve the following equations

  X  +  y  = 4  ………. ×2

 3x –2 y = 7   ………...×1

2 x + 2 y = 8

3 x – 2 y = 7    add

5 x  = 15

   X = 3

………..

the same ……….

the solution to this equations = {(3, 1)} 

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Example 3 :Solve the following equations

   X +  y  =  5 ……… ×4

   x – 4 y = 10 ………×1

      4 x + 4 y = 20

    X   - 4 y  = 10

    …………..

the same ……….

the solution to this equations = {(6,-1)} 

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Example 4: Two numbers equal to 7  ,  four  times the first number is greater than three times of  the second by 14

Find the two numbers

the answer :

let the two numbers is  X  and y

then :

    x  +  y =7  ……….. ×3   

 4x – 3 y = 14  ……….. ×1 

    3 x  + 3 y = 21

    4 x  - 3 y  = 14

    7 x     =  ………

       X = ….  

the same……….

The two numbers is 5 , 2

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Example 5 :

Solve the following equations

   X + 2 y  =  7 ………… ×3

   x – 3 y = 2   …….……×2

      3 x + 6 y = 21

    2 X   -  6y  = 4

    5 x   = 25

       X = 5

   5 + 2 y = 7

   2 y = 7 – 5

  2 y = 2

    Y = 1

the solution to this equations = {(5, 1)}