The solution set of the inequation 3 x+5 y<7 is - Vidyadip

MCQ

The solution set of the inequation $3 x+5 y<7$ is

A
whole $x y$-plane except the points lying on the line $3 x+5 y=7$.
B
whole $x y$-plane along with the points lying on the line $3 x+5 y=7$.
C
open half plane containing the origin except the points of line $3 x+5 y=7$.
D
open half plane not containing the origin.

✓

Answer

(c) : Given inequation is $3 x+5 y<7$
Let us draw the graph of $3 x+5 y=7$

$x$	0	2.33
$y$	1.4	0

Substitute, $x=0$ and $y=0$ in the inequation, we get
$
3(0)+5(0)<7
$
i.e., $0<7$ which is true.

$\therefore \quad$ The solution set of the inequality is an open half plane containing the origin except the points on line $3 x+5 y=7$

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