Class 6 Maths Algebra Equation

Equation

Equation is a condition on a variable. It is satisfied only for a definite value of a variable. For e.g. Equation 2y = 8 can only be satisfied when y =4.

It is to be noted that an equation has an equal sign (=) between its two sides. The    equation thus reflects that the value of the left hand side (LHS) is equal to the value of the right hand side (RHS). It is not possible to construct an equation without an equal sign. Since an equation has equal to sign, it can be solved to find out the value of a variable. The value of the variable in an equation which satisfies the equation is called a solution to the equation. If we get:

      2y = 20

      y = 20/2

      y = 10

y = 10 is a solution to the equation given.

 

If both the sides of an equation contain numbers then it is called a numerical equation. For e.g. : 4/2 = 2.

 

Problem: Complete the entries in the third column of the table.

Solution:

y = 10 is not a solution to the given equation because it does not satisfy both the side.

       Putting y =10 in the LHS of the equation, we get:

       10y

     = 10*10

     = 100

 

But RHS given in the equation is 80. Hence , y=10 is not a solution.

y = 8 is a solution of the given equation. Putting y= 8 in the LHS of the equation , we get       10y

   = 10*8

   = 80

 

The RHS given in the equation is also 80. Hence y=8 is a solution to the given equation.

 

Problem: Pick out the solution from the values given in the bracket next to each equation. Show that the other values do not satisfy the equation.  (a) 5m = 60    (10, 5, 12, 15)

Solution:

Solving the equation to get the value of m, we get :

          m = 60/5

          m = 12

Hence, m = 12 is the solution to the equation. The other values of m when put in the equation do not lead to RHS =60. This can be proved as follows :

  • When m = 10

   5m

= 5(10)

= 50

  • When m = 5

    5m

= 5(5)

= 25

  • When m = 15

   5m

= 5(15)

=75

 

Thus, none of these values of m give RHS as 60.

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