Elimination Method

Q.

x - y - 7 = 0,

x + y - 11 = 0

Sol.

x - y = 7

x + y = 11

….. (i)

….. (ii)

Adding (i) and (ii)

x - y = 7

x + y = 11

2x

= 18

x = 9

Substituting x = 9 in (ii)

9 + y = 11

y = 11 - 9

y = 2

x = 9 and y = 2 is the solution of the given simultaneous equations

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What does the word Elimination mean ?

Elimination means Removing

In this method

Keep variables on L.H.S and

Constant on R.H.S

What to remove ?

When the signs are same we subtract the two equations

Remove any one variable

For e.g. either remove ‘X’ or remove ‘Y’

And when the signs are different we add the two equations

Check the coefficient of the variable

We need to either remove x or remove y

Which variable can be removed ?

Whichever variable’s coefficient is same

Here coefficent of x as well as coefficent of y is same

To remove x, we need to subtract

As Signs are same

To remove y, we need to Add

As Signs are different

Since it is simple to add

Let us add the two equation

How to get the value of ‘y’ ?

We have to substitute x = 9

Either equation (i) or equation (ii)

How to eliminate ?

Either by adding or subtracting