Question

The pair of equation are 7x+8ky-16=0 and 14x+112y-21=0 . Find the value of k for which the system is inconsistent

Answer 1

Step-by-step explanation:

The lines are said to be inconsistent if,

$\frac{a1}{a2} = \frac{b1}{b2} \: and \: not \: equal \: to \: \frac{c1}{c2}$

Comparing the given equations with general form we get

$a1 = 7 \: \: \: \: \: \: a2 = 14 \: \: \: \: \: \: b1 = 8k \: \: \: \: \: \: b2 = 112$

Since

$\frac{a1}{a2} = \frac{b1}{b2}$

$\frac{7}{14} = \frac{8k}{112}$

$=> \frac{7 \times 112}{14 \times 8} = k$

$= > k = 7$

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