we know that
If a point is a solution of the inequality
then
The point must satisfy the inequality
we have
[tex]y\leq -x+1[/tex]
The solution of the inequality is the shaded area below the solid red line
see the attached figure to better understand the problem
Step 1
Point [tex]A(2,3)[/tex]
Substitute the value of x and the value of y in the inequality
[tex]x=2\ y=3[/tex]
[tex]3\leq -2+1[/tex]
[tex]3\leq -1[/tex] -------> is not true
therefore
The point A is not a solution for the inequality
See the attached figure------> the point A is not on the shaded area
Step 2
Point [tex]B(3,-2)[/tex]
Substitute the value of x and the value of y in the inequality
[tex]x=3\ y=-2[/tex]
[tex]-2\leq -3+1[/tex]
[tex]-2\leq -2[/tex] -------> is true
therefore
The point B is a solution for the inequality
See the attached figure------> the point B is on the shaded area
Step 3
Point [tex]C(2,1)[/tex]
Substitute the value of x and the value of y in the inequality
[tex]x=2\ y=1[/tex]
[tex]1\leq -2+1[/tex]
[tex]1\leq -1[/tex] -------> is not true
therefore
The point C is not a solution for the inequality
See the attached figure------> the point C is not on the shaded area
Step 4
Point [tex]D(-1,3)[/tex]
Substitute the value of x and the value of y in the inequality
[tex]x=-1\ y=3[/tex]
[tex]3\leq 1+1[/tex]
[tex]3\leq 2[/tex] -------> is not true
therefore
The point D is not a solution for the inequality
See the attached figure------> the point D is not on the shaded area
the answer is
[tex]B(3,-2)[/tex]
