CBSE Class 10-Mathematics: Chapter – 3 Pair of Linear Equation in Two Variables Part 14 (For CBSE, ICSE, IAS, NET, NRA 2023)

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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