Linear Equation

Linear Equation in 2 Variables

Ax + By = C  or Ax - By = C 

Where A, B and C are Constants

            x & y are Variables.


Example 1 : 3x + 2y = 4 and 8x + 5y = 9 Find the Value of x & y.

Solution : We have to do same Constant for any one variable,

So, [ 3x+2y=4 ]    multiply this equation with 5 ---------- 15x+10y=20,

[8x+5y=9 ]    multiply this equation with 2 --------- 16x+10y=18,

Solve both equation:

             15x+10y=20

           - 16x+10y=18

              x            = -2 

so we get x = -2 ,we put the value of x in this " 3x+2y=4 " equation.

 3x+2y=4 

3(-2)+2y=4

2y=4+6

2y=10

y=5

Here x=-2 and y=5.


Example 2 : The total cost of 6 books and 4 pencils is 34 Rs. & that of  5 books & 5 pencils is 30 Rs.Find the cost of each book & pencil Respectively.

Solution : Price of book = x & Pencil = y

Here, 6 books and 4 pencils = 6x+4y=34

         5 books and 5 pencils = 5x+5y=30

Solve these 2 equations 

6x+4y=34 multiply this equation with 5 ---------- 30x+20y=170,

5x+5y=30 multiply this equation with 6 ---------- 20x+20y=120,

  30x+20y=170

- 20x+20y=120

  10x        = 50

x = 5

so we get x = 5 ,we put the value of x in this " 6x+4y=34 " equation.

6x+4y=34

6(5)+4y=34

4y=34-30

4y=4

y=1

So, cost of each book=x=5 & cost of each pencil=y=1 


Example 3 : A man has some hens & cows. If the Number of heads be 48 & Number of feets is 140. Find the Number of hens.

Solution : Hen = x & Cow = y

Feet of hen = 2x,  Feet of Cow = 4y.   So, Number of Feet be 140 = 2x+4y

Head of hen = x, Head of Cow = y  So, Number of heads be 48 = x+y

Solve both equations,

2x+4y=140  

x+y=48  multiply this equation with 2 -------- 2x+2y=96,

   2x+4y=140 

2x+2y =96

       2y = 44

         y = 22

Put y=22 in x+y=48

x=48-22

x=26

So Number of hens = 26

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