Question

Among the given coordinates that satisfy the inequality $2y+x>1$ is (solve using graphs).

• A. (2,2)
• B. (-2,2)
• C. (-2,-2)

Answer 1

The correct option is C (-2,-2)

Given inequality

$2y+x<1$

Let us consider line $2y+x=1$

When $x=0$, $y=\frac{1}{2}$
$x=-1$, $y=11$

$2y+x=1$ is the line passing through the points (0,$\frac{1}{2}$) and (-1,1)

Representation on the graph:


From the graph choose two points say (2,2) and (-2,-2)

For (2,2),
$2y+x<1$
$\Rightarrow 2\times 2+2<1$
$\Rightarrow 6<1$
$6<1$ is false

For (-2,-2),
$2y+x>1$
$\Rightarrow -4-2>1$ $\Rightarrow -6>1$
$-6<1$ is True

Therefore, the region containing (-2,-2) is the required region.