Question

The pairs of linear equations whose solution is x = 2, y = –3 are

• A. x + y = –1 ; 2x – 3y = –5
• B. 2x + 5y = –11 ; 4x + 10y = –22
• C. 2x – y = 1 ; 3x + 2y = 0
• D. x – 4y –14 = 0 ; 5x – y – 13 = 0

Answer 1

Answer: (A), (D)

The correct options are
A

x + y = –1 ; 2x – 3y = –5

D

x – 4y –14 = 0 ; 5x – y – 13 = 0

x + y = –1 $\Rightarrow$ x = -1 - y......(i)

2x + 3y = –5........(ii)

Substituting (i) in (ii) we get

2 (-1 - y) + 3y = -5 $\Rightarrow$ y = -3

From (i)

x = -1- (-3)

= 2
(alternate method)

x - 4y = 14.....(i)

5x - y = 13.....(ii)

Substitute x = 2, y = –3 in the two given equations and check if it satisfies,

In (i) : 2 - 4(-3) = 14 (satisfies)

In (ii) : 5 (2) - (-3) = 13 (satisfies)