3) When a pair of linear equations of two variables represents two par

1.	3) When a pair of linear equations of two variables represents two parallel lines? Give an example.Anobaaf A
Answer» Consider the following pair of linear equations in two variables, x + 2y = 4 2x + 4y = 12 The solution of this pair would be a pair (x, y). Let’s find the solution, geometrically. The tables for these equations are: x04y = (4 – x)/220 x06y = (12 – 2x)/430 Now, take a graph paper and plot the following points: A(0, 2) B(4, 0) P(0, 3) Q(6, 0) Next, draw the lines AB and PQ as shown below. From the figure below, you can see that the two lines are parallel to each other. Therefore, these lines don’t intersect at all. Hence, this pair of equations has no solution.

3) When a pair of linear equations of two variables represents two parallel lines? Give an example.Anobaaf A

Answer»

Consider the following pair of linear equations in two variables,

x + 2y = 4

2x + 4y = 12

The solution of this pair would be a pair (x, y). Let’s find the solution, geometrically. The tables for these equations are:

x04y = (4 – x)/220

x06y = (12 – 2x)/430

Now, take a graph paper and plot the following points:

A(0, 2)

B(4, 0)

P(0, 3)

Q(6, 0)

Next, draw the lines AB and PQ as shown below.

From the figure below, you can see that the two lines are parallel to each other. Therefore, these lines don’t intersect at all. Hence, this pair of equations has no solution.

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