Answer:
(0,5)
Step-by-step explanation:
we have
[tex]2x+3y > 12[/tex] ----> inequality A
[tex]x-y\leq 1[/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 of the system (makes true both inequalities)
Verify each ordered pair
Substitute the value of x and the value of y of each ordered pair in the inequality A and in the inequality B and then compare the results
case 1) (0,5)
For x=0,y=5
Inequality A
[tex]2(0)+3(5) > 12[/tex]
[tex]15 > 12[/tex] ----> is true
so
The ordered pair satisfy inequality A
Inequality B
[tex]0-5\leq 1[/tex]
[tex]-5\leq 1[/tex] ---> is true
so
The ordered pair satisfy inequality B
therefore
The ordered pair would be a solution of the system
case 2) (5,2)
For x=5,y=2
Inequality A
[tex]2(5)+3(2) > 12[/tex]
[tex]16 > 12[/tex] ----> is true
so
The ordered pair satisfy inequality A
Inequality B
[tex]5-2\leq 1[/tex]
[tex]3\leq 1[/tex] ---> is not true
so
The ordered pair not satisfy inequality B
therefore
The ordered pair is not a solution of the system
case 3) (0,4)
For x=0,y=4
Inequality A
[tex]2(0)+3(4) > 12[/tex]
[tex]12 > 12[/tex] ----> is not true
so
The ordered pair not satisfy inequality A
therefore
The ordered pair is not a solution of the system
case 4) (6,0)
For x=6,y=0
Inequality A
[tex]2(6)+3(0) > 12[/tex]
[tex]12 > 12[/tex] ----> is not true
so
The ordered pair not satisfy inequality A
therefore
The ordered pair is not a solution of the system
