Question

A pair of linear equations which has a unique solution x = 2, y = –3 is ______.

विकल्प

• x + y = –1, 2x – 3y = –5

• 2x + 5y = –11, 4x + 10y = –22

• 2x – y = 1, 3x + 2y = 0

• x – 4y –14 = 0, 5x – y – 13 = 0

Answer 1

A pair of linear equations which has a unique solution x = 2, y = –3 is 2x + 5y = –11, 4x + 10y = –22 and x – 4y –14 = 0, 5x – y – 13 = 0.

Explanation:

For option (A),

L.H.S. = x + y = 2 + (-3) = −1 = R.H.S.

and 

L.H.S. = 2x − 3y = 2(2) − 3(−3) = 4 + 9 = 13 ≠ R.H.S.

:. does not satisfy the equation.

For option (B),

L.H.S. = 2x + 5y = 2(2) + 5(−3)

= 4 − 15 = −11 = R.H.S.

and L.H.S. = 4x + 10y = 4(2) + 10(−3)

= 8 − 30 = −22 = R.H.S.

Since x = 2, y = −3 satisfy the equations in option (B). 

x = 2, y = −3 is a unique solution of these equations.

For option (C),

L.H.S. = 2x − y = 2(2) − (−3) = 4 + 3 = 7 ≠ R.H.S.

and

L.H.S. = 3x + 2y = 3(2) + 2(−3) = 6 − 6 = 0 = R.H.S.

x = 2, y = −3 does not satisfy the equation. 

For option (D),

L.H.S. = x − 4y − 14 = 2 − 4 (−3) −14 = 2 + 12 − 14 

= 14 − 14 = 0 = R.H.S.

and L.H.S. = 5x − y − 13 = 5(2) − (−3) − 13

= 10 + 3 − 13 = 0 = R.H.S.

x = 2, y = −3 satisfy the equations in option (D)