we will proceed to resolve each case to determine the solution
we have
[tex]y-2x \leq -3[/tex]
[tex]y\leq2x-3[/tex]
we know that
If an ordered pair is the solution of the inequality, then it must satisfy the inequality.
case a) [tex](5,-3)[/tex]
Substitute the value of x and y in the inequality
[tex]-3\leq2*5-3[/tex]
[tex]-3\leq7[/tex] -------> is true
so
The ordered pair [tex](5,-3)[/tex] is a solution
case b) [tex](0,-2)[/tex]
Substitute the value of x and y in the inequality
[tex]-2\leq2*0-3[/tex]
[tex]-2\leq-3[/tex] -------> is False
so
The ordered pair [tex](0,-2)[/tex] is not a solution
case c) [tex](-6,-3)[/tex]
Substitute the value of x and y in the inequality
[tex]-3\leq2*-6-3[/tex]
[tex]-3\leq-15[/tex] -------> is False
so
The ordered pair[tex](-6,-3)[/tex] is not a solution
case d) [tex](1,-1)[/tex]
Substitute the value of x and y in the inequality
[tex]-1\leq2*1-3[/tex]
[tex]-1\leq-1[/tex] -------> is True
so
The ordered pair [tex](1,-1)[/tex] is a solution
case e) [tex](7,12)[/tex]
Substitute the value of x and y in the inequality
[tex]12\leq2*7-3[/tex]
[tex]12\leq11[/tex] -------> is False
so
The ordered pair [tex](7,12)[/tex] is not a solution
Verify
using a graphing tool
see the attached figure
the solution is the shaded area below the line
The points A and D lies on the shaded area, therefore the ordered pairs A and D are solution of the inequality
