Question

How many solutions does this set include?

• A. $5$
• B. $10$
• C. $20$
• D. Infinite

Answer 1

The correct option is D Infinite

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, $y\ge 0$ includes the region above the x axis.

$x=3⟹$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 not a closed region or it is not bounded. Hence, there are infinite number of solutions.