Question

Find the value of k if the pair of equations x +2y =3 & 5x + y =4 is inconsistent.

Answer 1

The pair of linear Equation is a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0

For Parallel Lines is inconsistent,

then, $\frac{a1}{a2} = \frac{b1}{b2} ≠ \frac{c1}{c2}$

The given equation is x + 2y = 3 and

5x + ky = 4

On Comparing with general form of pair of linear Equation in two variables x and y is

a1 = 1, b1 = 2, c1 = -3, a2 = 5, b2 = k, c2 = -4

$\frac{1}{2} = \frac{2}{k} ≠ \frac{ - 3}{ - 4}$

$=> \frac{1}{2} = \frac{2}{k}$

$=> k = 4$

For, k = 4, the given system of has No Solution.

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