Answer:
Option d. [tex]4y+2x\leq -1[/tex]
Step-by-step explanation:
we know that
If a ordered pair is a solution of an inequality, then the ordered pair must be satisfy the inequality
Verify each case
case a) [tex]y\geq2x+8[/tex]
we have
[tex]x=5, y=-3[/tex]
Substitute the value of x and the value of y in the inequality and then compare the results
[tex]-3\geq2(5)+8[/tex]
[tex]-3\geq18[/tex] -----> is not true
therefore
the ordered pair is not a solution
case b) [tex]-2y<3x-9[/tex]
we have
[tex]x=5, y=-3[/tex]
Substitute the value of x and the value of y in the inequality and then compare the results
[tex]-2(-3)<3(5)-9[/tex]
[tex]6<6[/tex] -----> is not true
therefore
the ordered pair is not a solution
case c) [tex]y-2x>5[/tex]
we have
[tex]x=5, y=-3[/tex]
Substitute the value of x and the value of y in the inequality and then compare the results
[tex]-3-2(5)>5[/tex]
[tex]-13>5[/tex] -----> is not true
therefore
the ordered pair is not a solution
case d) [tex]4y+2x\leq -1[/tex]
we have
[tex]x=5, y=-3[/tex]
Substitute the value of x and the value of y in the inequality and then compare the results
[tex]4(-3)+2(5)\leq -1[/tex]
[tex]-2\leq -1[/tex] -----> is true
therefore
the ordered pair is a solution
