NCERT Solutions
Class 10 Maths
Pair of Linear Equations in Two Variables

Ex.3.1 Q.3
On comparing the ratios ,
and
, find out whether the following pair of linear equations are consistent,
or inconsistent.
(1) 3x + 2y = 5; 2x – 3y = 7
(2) 2x – 3y = 8; 4x – 6y = 9
(3) x +
y = 7; 9x – 10y = 14
(4) 5x – 3y = 11; -10x + 6y = –22
(5) x + 2y =8; 2x + 3y = 12
(1) 3x + 2y = 5; 2x – 3y = 7
=
= -
and
=
Hence, ≠
These linear equations intersect each other at one point and therefore have only one possible solution.
Hence, the pair of linear equations is consistent.
(2) 2x – 3y = 8; 4x – 6y = 9
=
=
=
=
=
Hence, =
≠
Therefore, these linear equations are parallel to each other and thus have no possible solution.
Hence, the pair of linear equations is inconsistent.
(3) x +
y = 7; 9x – 10y = 14
= (3 ÷ 2) ÷ 9 =
= (5 ÷ 3) ÷ (-10) = –
=
=
Hence, ≠
Therefore, these linear equations intersect each other at one point and thus have only one possible solution.
Hence, the pair of linear equations is consistent.
(4) 5x – 3y = 11; – 10x + 6y = –22
=
= –
= –
= –
=
= –
Hence, =
=
Therefore, these linear equations are coincident and have infinite number of possible solutions.
Therefore, the pair of linear equations is consistent.
(5) x + 2y =8; 2x + 3y = 12
=
=
=
and
=
=
Hence, =
=
Therefore, these linear equations are coincident and have infinite number of possible solutions.
Therefore, the pair of linear equations is consistent.