CAT 2024 Slot 3 QA Question 11: For some constant real numbers $p$, $k$ and $a$, consider the following system of linear equations in $x$ and $y$:
$px - 4y = 2$
$3x + ky = a$
A necessary condition for the system to have no solution

Question

For some constant real numbers $p$, $k$ and $a$, consider the following system of linear equations in $x$ and $y$:
$px - 4y = 2$
$3x + ky = a$
A necessary condition for the system to have no solution

Accepted Answer

For two linear equations in two variables to have no solution, the two lines must be parallel but not identical.

Parallel lines require proportional coefficients of $x$ and $y$.

$\dfrac{p}{3} = \dfrac{-4}{k}$

For the lines not to be identical, the constants must not be in the same ratio.

$\dfrac

For some constant real numbers ppp, kkk and aaa, consider the following system of linear equations in xxx and yyy: px−4y=2px - 4y = 2px−4y=2 3x+ky=a3x + ky = a3x+ky=a A necessary condition for the system to have no solution for (x,y)(x,y)(x,y), is

For some constant real numbers $p$ , $k$ and $a$ , consider the following system of linear equations in $x$ and $y$ : $px - 4y = 2$ $3x + ky = a$ A necessary condition for the system to have no solution for $(x,y)$ , is