##### Do the following pair of linear equations have no solution? Justify your answer.(i) 2x + 4y = 3 and 12y + 6x = 6(ii) x = 2y and y = 2x(iii) 3x + y - 3 = 0 and

The Condition for no solution is : (parallel lines)

(i) Yes.

Given pair of equations are,

2x+4y - 3 = 0 and 6x + 12y - 6 = 0

Comparing with ax+ by +c = 0;

Here, a1 = 2, b1 = 4, c1 = - 3;

And a2 = 6, b2 = 12, c2 = - 6;

a1 /a2 = 2/6 = 1/3

b1 /b2 = 4/12 = 1/3

c1 /c2 = - 3/ - 6 = 1/2

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

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

(ii) No.

Given pair of equations,

x = 2y and y = 2x

or x - 2y = 0 and 2x - y = 0;

Comparing with ax + by + c = 0;

Here, a1 = 1, b1 = - 2, c1 = 0;

And a2 = 2, b2 = - 1, c2 = 0;

a1 /a2 = 1/2

b1 /b2 = -2/-1 = 2

Here, a1/a2 b1/b2.

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

(iii) No.

Given pair of equations,

3x + y - 3 = 0

and

Comparing with ax + by + c = 0;

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

And a2 = 2, b2 = 2/3, c2 = - 2;

a1 /a2 = 2/6 = 3/2

b1 /b2 = 4/12 = 3/2

c1 /c2 = - 3/-2 = 3/2

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

Hence, the given pair of linear equations is coincident and having infinitely many solutions.

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