The pairs of linear equations which have the unique solution x = 2 , y = – 3 are, Options: A . &nbsp x + y = – 1 ; 2 x + 3 y = – 5 B . &nbsp 2 x + 5 y = – 11 ; 4 x + 10 y = – 22 C . &nbsp 2 x – y = 1 ; 3 x + 2 y = 0 D . &nbsp x – 4 y – 14 = 0 ; 5 x – y – 13 = 0

The pairs of linear equations which have the unique solution x=2,y=

Question

The pairs of linear equations which have the unique solution $x = 2, y = - 3$ are,

Options:

A .

x + y = - 1; 2 x + 3 y = - 5

B .

2 x + 5 y = - 11; 4 x + 10 y = - 22

C .

2 x - y = 1; 3 x + 2 y = 0

D .

x - 4 y - 14 = 0; 5 x - y - 13 = 0

Answer: Option A
:
A and D

Option A:
$x + y = - 1 - - - - - (i)$
$2 x + 3 y = - 5 - - - - (i i)$
$(i) \times 2 \to 2 x + 2 y = - 2 - - - - (i i i)$
Solving by elimination $((i i i) - (i i))$ we get,
$x = 2 a n d y = - 3.$
Option D:
$x - 4 y = 14 - - - - (i)$

$5 x - y = 13 - - - - - (i i)$
$(i i) \times 4 \to 20 x - 4 y = 52 - - - - (i i i)$

Solving by elimination method $((i i i) - (i))$ we get,

$x = 2 a n d y = - 3$

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