Question

Which quadrant does the solution lie in?

• A. $I$
• B. $II$
• C. $III$
• D. $IV$

Answer 1

The correct option is A $I$

Given, $2x+3y>2$

$x-y<0⟹y>x$

$y\ge 0$

$x\le 3$

first, draw the graph for equations $2x+3y=2$

$x-y=0⟹x=y$

$y=0⟹x-axis$

$x=3$

$x=y$ is the line which passes through the origin as shown in the above fig

Hence, $y>x$ includes the above region of the line.

$y=0⟹x-axis$. Hence, $x\le 3$ includes the left region of the line.

$x=3⟹$line parallel to x-axis. Hence, $x\le 3$ includes the left region of the line.

for $2x+3y=2$

substituting y=0, we get $2x=2⟹x=1$

substituting x=0, we get $3y=2⟹y=\frac{2}{3}$

Therefore, line $2x+3y=2$ passes through (1,0) and (0,2/3) as shown in the above figure

Hence, $2x+3y>2$ includes the above region of the line.

Therefore, the blue shaded region is the feasible region which is present in I quadrant as shown in the figure.