Question

Write the value of k for which the system of equations x+ y – 4 = 0 and 2x + ky -3 =0 has no solution

Answer 1

✿solution ✿

the given system of equation is

$x + y - 4 = 0 - - - - (1) \\ 2x + ky - 3 = 0 - - - - - (2)$

these equations are form

$a1x + b1y + c1 = 0 \: \: and \: \: a2x + b2y + c2 = 0$

where

$a1 = 1.b1 = 1.c1 = - 4 \\ a2 = 2.b2 = k.c2 = - 3$

let , the given system of equations have no solution

then ,

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

$\frac{1}{2} = \frac{1}{k} not \: equal \: \frac{ - 4}{ - 3}$

k= 2