Question

For what value of k is the pair of equation : 8x + 5y = 9; kx + 10y = 15 inconsistent?

Answer 1

$\huge\boxed{\underline{\underline{\green{Solution}}}}$

FORMULA TO BE IMPLEMENTED :

A pair of Straight Lines

$\displaystyle \: a_1x+b_1y+c_1=0 \: and \: \: a_2x+b_2y+c_2=0$

is said to be inconsistent if $\displaystyle \: \: \frac{a_1}{a_2} = \frac{b_1}{b_2}$

TO DETERMINE

The value of k so that

$8x +5y = 9 \: \: and \: \: kx + 10y =15 \: are \: inconsistent$

CALCULATION :

Given pair of linear equations

$8x +5y = 9 \: \: and \: \: kx + 10y =15$

Comparing with

$\displaystyle \: a_1x+b_1y+c_1=0 \: and \: \: a_2x+b_2y+c_2=0$

We get

$\displaystyle \: a_1 = 8 \: , \: b_1 = 5 \: , c_1= - 9 \: \: and \: \: a_2 = k \: , \: b_2 = 10\: , \: \: c_2= - 15$

So the pair of equations are inconsistent if

$\displaystyle \: \: \frac{a_1}{a_2} = \frac{b_1}{b_2}$

$\implies \: \displaystyle \: \: \frac{8}{k} = \frac{5}{10}$

$\implies \:5k = 80$

$\implies \:k = 16$

RESULT

The required value of k is 16