A pair of linear equations which has a unique solution $ x=2, y=-3 $ is
(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 $
Given:
A unique solution \( x=2, y=-3 \).
To do:
We have to find the pair of linear equations which has the unique solution \( x=2, y=-3 \).
Solution:
If $x = 2, y = - 3$ is a unique solution of any pair of equations, then these values must satisfy the pair of equations.
For option (b),
$2x+ 5y= -11$
LHS $= 2x + 5y$
$= 2(2) + 5(-3)$
$= 4 - 15$
$= -11$
$=$ RHS
$4x + 10y = -22$
LHS $= 4x + 10y$
$= 4(2) + 10(-3)$
$= 8 - 30$
$= -22$
$=$ RHS
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