Q. 4

# For what value of k will the following pair of linear equations have no solution?

2x + 3y = 9, 6x + (k – 2) y = (3k – 2) .

Answer :

There are two equations given in the question:

2x + 3y – 9 = 0 (i)

And, 6x + (k – 2)y – (3k – 2) = 0 (ii)

These given equations are in the form a_{1}x + b_{1}y + c_{1} = 0 and a_{2}x + b_{2}y + c_{2} = 0 where,

a_{1} = 2, b_{1} = 3 and c_{1} = – 9

Also, a_{2} = 6, b_{2} = (k – 2) and c_{2} = – (3k – 2)

Now, for the given pair of linear equations having no solution we must have:

,

k = 11,

k = 11, 3 (3k – 2) 9 (k – 2)

∴ k = 11 and 1 3 (True)

Hence, the value of k is 11

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