Question

1. If a pair of equation is consistent, then the lines will be
(a) parallel
(b) always coincident (c) always intersecting
(d) intersecting or coincident

Answer 1

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If a pair of linear equation is consistent, then it has unique solutions and infinity solutions.

For unique solution-

⇒  

a  

2

​  

 

a  

1

​  

 

​  

 



​  

=  

b  

2

​  

 

b  

1

​  

 

​  

 

∴ the lines will be intersecting.

For infinity solution-

⇒  

b  

1

​  

 

a  

1

​  

 

​  

=  

b  

2

​  

 

b  

1

​  

 

​  

=  

c  

2

​  

 

c  

1

​  

 

​  

 

∴ the lines will be coincident.

Answer 2

Answer: d) intersecting or coincident

Two equations being consistent means the two equations have 'at least' one (can also beire than one) common solution which is only there in the case intersecting or coincident lines therefore the answer is INTERSECTING OR COINCIDENT

Hope it helps (◠‿◕)

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