Answer:
(12,-6)
Step-by-step explanation:
we have
[tex]y\leq \frac{4}{3}x+5[/tex] ----> inequality A
[tex]y\geq -\frac{5}{2}x+5[/tex] ---> inequality B
we know that
If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities (makes true both inequalities)
Verify each point
Substitute the value of x and the value of y of each ordered pair in the inequality A and in the inequality B
case 1) (0,-1)
Inequality A
[tex]-1\leq \frac{4}{3}(0)+5[/tex]
[tex]-1\leq5[/tex] ----> is true
Inequality B
[tex]-1\geq -\frac{5}{2}(0)+5[/tex]
[tex]-1\geq 5[/tex] ----> is not true
therefore
The ordered pair is not a solution of the system
case 2) (0,3)
Inequality A
[tex]3\leq \frac{4}{3}(0)+5[/tex]
[tex]3\leq5[/tex] ----> is true
Inequality B
[tex]3\geq -\frac{5}{2}(0)+5[/tex]
[tex]3\geq 5[/tex] ----> is not true
therefore
The ordered pair is not a solution of the system
case 3) (-6,-6)
Inequality A
[tex]-6\leq \frac{4}{3}(-6)+5[/tex]
[tex]-6\leq-3[/tex] ----> is true
Inequality B
[tex]-6\geq -\frac{5}{2}(-6)+5[/tex]
[tex]-6\geq 20[/tex]----> is not true
therefore
The ordered pair is not a solution of the system
case 4) (12,-6)
Inequality A
[tex]-6\leq \frac{4}{3}(12)+5[/tex]
[tex]-6\leq21[/tex] ----> is true
Inequality B
[tex]-6\geq -\frac{5}{2}(12)+5[/tex]
[tex]-6\geq -25[/tex] ----> is true
therefore
The ordered pair is a solution of the system (makes true both inequalities)
