Linear Equations with two variable(2)

the method of elimination""

Example 1 : 

  Solve the following equations

 , x+ y = 8 , 2x – y = 1

the answer :

x+ y = 8

2x – y = 1   

3 x = 9

X=9 /3 

X =3

Put value of x  in  

x+ y= 8

3 + y = 8

Y =8 – 3

Y = 5

the solution to this equations = {(3 , 5)}

Example 2:

 Solve the following equations

  , x+ y = 7, 4x – y = 8

the same ……….

the solution to this equations = {(3, 4)}

Example 3:

 Solve the following equations

 , x+ y = 5 , 3 x – y = 11

the same ……….

the solution to this equations = {(4,1)}

  

Example 4:

 Two numbers equal to 12 ,   

 Three times the first number

 is greater than the second by 8

Find the two numbers

the answer :

let the two numbers is  X  and y

then : x + y =12  ,  3x – y = 8

the same……….

The two numbers is 5 , 7

 Example 5 :

   The perimeter of the rectangle

  , is equal to 22 cm
The difference between his two

 dimensions equals 3 cm

 Two dimensions   Find the

the answer :

      let the two dimensions  

    is  X  and y

then :  x + y =11( half perimeter)   

           , x – y = 3

the same……….

 the two dimensions 

   is  7 cm  and  4 cm