91Ó°ÊÓ

The steps to graph the inequality are provided below.

1. If the inequality contains greater than or less than sign then the boundary of the line will be dashed. If the inequality contains signs of greater than or equal to or less than or equal to then the boundary of the line will be solid.

2. Select a point (known as test point) from the plane that does not lie on the boundary on the line and substitute it in the inequality.

3. If the inequality is true then shade the region that contains the test point otherwise shade the other region when inequality is false.

For the region to be a square in Quadrant I, take inequalities that lie in quadrant I. Since, square has all four sides equal so inequalities have to be at same distance from one other. Consider the system of inequalities provided below.

$\begin{array}{l}2≤x≤4\\ 2≤y≤4\end{array}$

These can be written as $2≤x,x≤4,2≤y\text{and}y≤4$

Therefore, all the boundary lines will be solid.

Graph the inequalities $2≤x,x≤4,2≤y\text{and}y≤4$on same plane and shade the region.

The corresponding equation is $2=x$.

Take a test point that does not lie on the boundary of the line, say $\left(0,0\right)$.

Substitute the point $\left(0,0\right)$in the inequality and check whether it’s true or not.

$2≤0$

This is false.

Therefore, shade the region not containing the point $\left(0,0\right)$.

The corresponding equation is $x=4$.

Take a test point that does not lie on the boundary of the line, say $\left(0,0\right)$.

Substitute the point $\left(0,0\right)$in the inequality and check whether it’s true or not.

$0≤4$

This is true.

Therefore, shade the region containing the point $\left(0,0\right)$.

The corresponding equation is $y=2$.

Take a test point that does not lie on the boundary of the line, say $\left(0,0\right)$.

Substitute the point $\left(0,0\right)$in the inequality and check whether it’s true or not.

$2≤0$

This is false.

Therefore, shade the region not containing the point $\left(0,0\right)$.

The corresponding equation is $y=4$.

Take a test point that does not lie on the boundary of the line, say $\left(0,0\right)$.

Substitute the point $\left(0,0\right)$in the inequality and check whether it’s true or not.

$0≤4$

This is true.

Therefore, shade the region containing the point $\left(0,0\right)$.

Thus, the shaded regions are provided below.

The region 1 and region 3 corresponds to inequality $2≤x≤4$.

The region 2 and region 3 corresponds to inequality $2≤y≤4$.

The region common to both the inequalities $2≤x≤4$and $2≤y≤4$is Region 3.

Hence, the solution to the system of inequalities are the ordered pairs lying in the shaded region. The shaded region represent a square in Quadrant I.