Do the following equations represent a pair of coincident lines? Justify your answer.(i) and 7x + 3y = 7(ii) - 2x - 3y = 1 and 6y + 4x = - 2(iii)

Condition for coincident lines,

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

(i) No.

Given pair of linear equations

and 7x + 3y = 7

Comparing 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 with ax + by + c = 0;

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

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

a1 /a2 = - 2/4 = - 1/2

b1 /b2 = - 3/6 = - 1/2

c1 /c2 = - 1/2

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

Hence, the given pair of linear equations is coincident.

(ii) No, given pair of linear equations are

and = 0

Comparing with ax + by + c = 0;

Here, a1 = 1/2, b1 = 1, c1 = 2/5;

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.

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