Question

Solve : 99x+101y=499
101x+99y=501

Answer 1

Given system of equations are,

99x+101y=499........[1]

and 101x+99y=501.........[2]

Adding the equations [1] and [2],

(101x+99y)+(99x+101y)=501+499

→200x+200y=1000

→200(x+y)=1000

→x+y=5..........[3]

Subtracting equations [2] and [1],

(101x+99y)-(99x+101y)=501-499

→2x-2y=2

→x-y=1.........[4]

Adding [3] and [4],

(x+y)+(x-y)=5+1

→2x=6

→x=3

Substituting x=3 in [3],

x+y=5

→y=5-x

→y=5-3

→y= 2

Hence,(x,y)=(3,2)

Answer 2

Given :-

The pair of linear equations are:-

• 99x + 101y = 499
• 101x + 99y = 501

To Find :-

• The value of x & y from the given pair of linear equations

Solution :-

Let,

• 99x + 101y = 499......( 1 )
• 101x + 99y = 501.......( 2 )

Adding equation ( 1 ) & ( 2 ), we get,

⇒ 200x + 200y = 1000

⇒ x + y = 5......( 3 )

Equation ( 1 ) - equation ( 2 ) gives,

⇒ -2x + 2y = -2

⇒ -x + y = -1.....( 4 )

Now, adding equation ( 3 ) & ( 4 ) gives,

⇒ 2y = 4

⇒ y = 4/2

⇒ y = 2

Substituting the value of y in ( 3 ) gives,

⇒ x + 2 = 5

⇒ x = 5 - 2

⇒ x = 3

Hence,

• Value of x = 3.
• Value of y = 2.