What are consistent and inconsistent equations? State which type of equations are Intersecting, Coincident And Parallel equations are consistent or inconsistent?
Answers
Answer:
Hint: Check for the conditions of unique solutions and infinity solutions if pair of straight lines is in form of
a1x+b1y=c1
a2x+b2y=c2
In the question, we are given that if a pair of linear equations is consistent then we have to point out the type of lines it is from the options given.
Before concluding about the answer or which option is correct, we will tell or explain about the term consistent. Lines which intersect at a point which represents the unique solution of the system in two variables. Generally, system of pair of straight lines are represented by a1x+b1y+c1=0 and a2x+b2y+c2=0.
In other languages the pair of lines will coincide either or intersect at one point, then the pair of lines will be consistent. Otherwise, they will be considered as consistent.
We check the pair of lines coincide or not using the condition that,
a1b2=b1b2=c1c2
If the above condition satisfies then the lines are considered as consistent as it means the pair of lines are coincident.
There is also another condition that is represented as
a1b2≠b1b2
If the above condition satisfies then the lines are considered as consistent as it means the pair of lines are intersecting.
So, the correct option is ‘C’.
Note: If the pair of straight lines are parallel then, the lines will be considered as inconsistent their condition will be,
a1a2=b1b2≠c1c2
Answer:
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Explanation:
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