Question

2. Do the following equations represent a pair of coincident lines? Justify your answer.
(i) 3x + 1/7y = 3
7x + 3y = 7
(ii) –2x – 3y = 1
6y + 4x = – 2
(iii) x/2 + y + 2/5 = 0
4x + 8y + 5/16 = 0

Answer 1

Answer:

Condition for coincident lines,

a1/a2 = b1/b2 = c1/c2;

(i) No.

Given pair of linear equations are:

3x + 1/7y = 3

7x + 3y = 7

Comparing the above equations with ax + by + c = 0;

Here, a1 = 3, b1 = 1/7, c1 = - 3;

And a2 = 7, b2 = 3, c2 = - 7;

a1 /a2 = 3/7

b1 /b2 = 1/21

c1 /c2 = - 3/ - 7 = 3/7

Here, a1/a2 ≠ b1/b2.

Hence, the given pair of linear equations has unique solution.

(ii) Yes,

Given pair of linear equations.

- 2x - 3y - 1 = 0 and 4x + 6y + 2 = 0;

Comparing the above equations with ax + by + c = 0;

Here, a1 = - 2, b1 = - 3, c1 = - 1;

And a2 = 4, b2 = 6, c2 = 2;

a1 /a2 = - 2/4 = - ½

b1 /b2 = - 3/6 = - ½

c1 /c2 = - ½

Here, a1/a2 = b1/b2 = c1/c2, i.e. coincident lines

Hence, the given pair of linear equations is coincident.

(iii) No,

Given pair of linear equations are

x/2 + y + 2/5 = 0

4x + 8y + 5/16 = 0

Comparing the above equations with ax + by + c = 0;

Here, a1 = ½, b1 = 1, c1 = 2/5;

NCERT Exemplar Solutions For Class 10 Maths Chapter 3-

Pair Of Linear Equations In Two Variables

And a2 = 4, b2 = 8, c2 = 5/16;

a1 /a2 = 1/8

b1 /b2 = 1/8

c1 /c2 = 32/25

Here, a1/a2 = b1/b2 ≠ c1/c2, i.e. parallel lines

Hence, the given pair of linear equations has no solution.

Answer 2

Answer:

0 is the answer

Step-by-step explanation: