Question

x+y=6 and x-y=3 then x,y =?

Answer 1

Here , the concept of solving Pair of linear equations in two variable arises .

Methods to solve pair of linear equations in two variable :-

( i ) Elimination Method

( ii ) Substitution Method

( iii ) Cross - Multiplication Method

Solution :-

Let, x + y = 6 - - - - ( a )

x - y = 3 - - - - ( b )

Adding ( a ) and ( b ) .

( x + y ) + ( x - y ) = 6 + 3

x + y + x - y = 9

Cancelling " y " From LHS .

2x = 9

x = 9/2

x = 4.5

Now , By ( a ) ,

x + y = 6

4.5 + y = 6

y = 6 - 4.5

y = 1.5

Hence , x = 4.5 , y = 1.5

Verification :-

By ( a )

x + y = 6

4.5 + 1.5 = 6

6 = 6

By ( b )

x - y = 3

4.5 - 1.5 = 3

3 = 3

Hence , Verified !