Question

The set of points $(x,y)$ satisfying the inequalities $x+y\le 1,-x-y\le 1$ lie in the region bounded by the two straight lines passing through the respective pair of points.

• A. $\left\{\right(1,0),(0,1\left)\right\}$ and $\left\{\right(-1,0),(0,-1\left)\right\}$
• B. $\left\{\right(1,0),(1,1\left)\right\}$ and $\left\{\right(-1,0),(0,-1\left)\right\}$
• C. $\left\{\right(-1,0),(0,-1\left)\right\}$ and $\left\{\right(1,0),(-1,1\left)\right\}$
• D. $\left\{\right(1,0),(0,-1\left)\right\}$ and $\left\{\right(-1,0),(0,1\left)\right\}$
• E. $\left\{\right(1,0),(1,1\left)\right\}$ and $\left\{\right(-1,0),(-1,-1\left)\right\}$

Answer 1

The correct option is A $\left\{\right(1,0),(0,1\left)\right\}$ and $\left\{\right(-1,0),(0,-1\left)\right\}$

Given constraints are
$x+y\le 1$
and $-x-y\le 1$
Assume these inequalities as equality and draw these lines on graph paper, we get
and $\begin{array}{c}x+y=1\\ x+y=-1\end{array}\}$
So, pair of points $\left\{\right(1,0),(0,1\left)\right\}$ and $\left\{\right(-1,0),(0,-1\left)\right\}$ are satisfying the inequalities
$x+y\le 1$ and $-x-y\le 1$.