Question

On comparing the ratios, find out whether the following pair of linear equations are consistent, or inconsistent.

Answer 1

(i) 3x + 2y = 5

2x − 3y = 7

These linear equations are intersecting each other at one point and thus have only one possible solution. Hence, the pair of linear equations is consistent.

(ii)2x − 3y = 8

4x − 6y = 9

Since ,

Therefore, these linear equations are parallel to each other and thus have no possible solution. Hence, the pair of linear equations is inconsistent.

(iii)

Since ,

Therefore, these linear equations are intersecting each other at one point and thus have only one possible solution. Hence, the pair of linear equations is consistent.

(iv)5x − 3 y = 11

− 10x + 6y = − 22

Since ,

Therefore, these linear equations are coincident pair of lines and thus have infinite number of possible solutions. Hence, the pair of linear equations is consistent.

(v)

Since

Therefore, these linear equations are coincident pair of lines and thus have infinite number of possible solutions. Hence, the pair of linear equations is consistent.