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CBSE Class 10- Mathematics: Chapter β 3 Pair of Linear Equation in Two Variables Part 14
Question 3:
On comparing the ratios , find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident:
(i)
(ii)
(iii)
Answer:
(i)
Comparing equation with and with ,
We get
We have
Because
Hence, lines have unique solution which means they intersect at one point.
(ii)
Comparing equation with and with ,
We get,
We have
Because
Hence, lines are coincident.
(iii)
Comparing equation with and with ,
We get,
We have
Because
Hence, lines are parallel to each other.
Question 4:
Given the linear equation , write another linear equation in two variables such that the geometrical representation of the pair so formed is:
(i) Intersecting lines
(ii) Parallel lines
(iii) Coincident lines
Answer:
Let the second line be equal to
Comparing given line with ,
We get and
Two lines intersect with each other if
So, second equation can be because
Let the second line be equal to
Comparing given line with ,
We get and
Two lines are parallel to each other if
So, second equation can be because
Let the second line be equal to
Comparing given line with ,
We get and
Two lines are coincident if
So, second equation can be because