we will proceed to resolve each case to determine the solution
we have
\(y-2x \leq -3\)
\(y\leq2x-3\)
we know that
If an ordered pair is the solution of the inequality, then it must satisfy the inequality.
case a) \((5,-3)\)
Substitute the value of x and y in the inequality
\(-3\leq2*5-3\)
\(-3\leq7\) -------> is true
so
The ordered pair \((5,-3)\) is a solution
case b) \((0,-2)\)
Substitute the value of x and y in the inequality
\(-2\leq2*0-3\)
\(-2\leq-3\) -------> is False
so
The ordered pair \((0,-2)\) is not a solution
case c) \((-6,-3)\)
Substitute the value of x and y in the inequality
\(-3\leq2*-6-3\)
\(-3\leq-15\) -------> is False
so
The ordered pair\((-6,-3)\) is not a solution
case d) \((1,-1)\)
Substitute the value of x and y in the inequality
\(-1\leq2*1-3\)
\(-1\leq-1\) -------> is True
so
The ordered pair \((1,-1)\) is a solution
case e) \((7,12)\)
Substitute the value of x and y in the inequality
\(12\leq2*7-3\)
\(12\leq11\) -------> is False
so
The ordered pair \((7,12)\) 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
