Question

Plot the region on the XY plane satisfying the inequality: |x| + lyl + |x + yl < 4
How many points with integer co-ordinates lie in the interior of this region?​

Answer 1

Answer:

$Given \: constraints \: are \\ </p><p>x \: + \: y≤1 \\ </p><p>and \: \\  − \: x \: − \: y \: ≤ \: 1 \\ </p><p>Assume these inequalities \\ as equality and draw \\ these lines on graph paper, we get \\ </p><p>and  \\ { \: x \: + \: y= \:1 \:  x \: + \: y \: = \: − \: 1} \\ </p><p>So, \\ pair \: of \: points  \: \\ {(1,0),(0,1)}  \\ and \\  (−1, \: 0 \: ),( \: 0 \: ,− \: 1 \: ) \\  are \: satisfying \: the \\ inequalities \\ </p><p>x \: + \: y \: ≤ \: 1  \\ and \\  − \: x \: − \: y \: ≤ \: 1.</p><p></p><p>$