B

C

A

D

3x+y=3 x-y=5

3x-y=3 x-y=5

2x+y=3 x+y=5

3x+y=3 x+y=5

A Pair of Linear Equations Which Has a Unique Solution x=2, y=-3 Is

By Team Aakash Byju's | 9th November 2022

The correct answer is   option D.

Detailed Explanation

3x+y=3  x-y=5

Let us consider each given option and substitute the values of x and y to check if they satisfy the equation or not.

Substitute  x=2 and  y=-3 in the given options A,B,C and D.

For A, equations are

3x+y=3 and x+y=5

Now substitute  x=2 and  y=-3 in the above equations.

3x+y=3 => 3(2)+(-3) = 3

=> 6 - 3 = 3 so, 3 = 3

x+y=5

=> -1 = 5 which is not true.

Hence, option A does not have the given unique solution.

=> 2 + (-3) = 5 => 2 - 3 = 5

For B, equations are

2x+y=3 and x+y=5

Now substitute  x=2 and  y=-3 in the above equations.

2x+y=3 => 2(2)+(-3) = 3

=> 4 - 3 = 3 => 1 = 3  which is not true.

x+y=5 => 2 + (-3) = 5

=> 2 - 3 = 5 => -1 = 5 which is not true.

Hence, option B does not have the given unique solution.

For C, equations are

3x-y=3 and x-y=5

Now substitute  x=2 and  y=-3 in the above equations.

3x-y=3 => 3(2)-(-3) = 3

=> 6 + 3 = 3 => 9 =3

x-y=5 => (2) - (-3) = 5

=> 2 + 3 = 5 => 5 = 5 which is not true.

Hence, option C does not have the given unique solution.

For D, equations are

3x+y=3 and x-y=5

Now substitute  x=2 and  y=-3 in the above equations.

3x+y=3 => 3(2)+(-3) = 3

=> 6 - 3 = 3 => 3 = 3

x-y=5 => (2) - (-3) = 5

=> 2 + 3 = 5 => 5 = 5 Both are true.

Hence, option D has the given unique solution.