Question

If 7x+5y=11 & 5x+7y=13

Answer 1

Given equation : 7x + 5y = 11     ...( i )

                            5x + 7y = 13     ...( ii )

Multiply by 5 on both sides of ( i ),

⇒ 5( 7x + 5y ) = 5( 11 )

⇒ 35x + 25y = 55         ...( iii )

Multiply by 7 on both sides of ( ii ),

⇒ 7( 5x + 7y ) = 7( 13 )

⇒ 35x + 49y = 91         ...( iv )

Now, subtract ( iii ) from ( iv ),

⇒ 35x + 49y - ( 35x + 25y ) = 91 - 55

⇒ 35x + 49y - 35x - 25y = 36

⇒ 24y = 36

⇒ y = 36 / 24

⇒ y = 3 / 2

Substitute the value of y in ( i )

⇒ 7x + 5y = 11

⇒ 7x + 5( 3 / 2 ) = 11

⇒ 7x + 15 / 2 = 11

⇒ 7x = 11 - 15 / 2

⇒ 7x = ( 22 - 15 ) / 2

⇒ 7x =7 / 2

⇒ x = 1 / 2

Therefore the value of x is 1 / 2 and value of y is 3 / 2

Answer 2

x=1/2 and y=3/2
7(1/2)+5(3/2)=11
5(1/2)+7(3/2)=13