Answer:
[tex](4,0)[/tex]
Step-by-step explanation:
we have
[tex]y<x-1[/tex] -----> inequality A
[tex]y>-x+2[/tex] -----> inequality B
we know that
If a ordered pair is a solution of the system of equations , then the ordered pair must satisfy both inequalities
Verify each case
case A) [tex](4,0)[/tex]
Inequality A
[tex]0<4-1[/tex]
[tex]0<3[/tex] ------> is true
Inequality B
[tex]0>-4+2[/tex]
[tex]0>-2[/tex] -------> is true
therefore
the ordered pair is a solution
case B) [tex](0,0)[/tex]
Inequality A
[tex]0<0-1[/tex]
[tex]0<-1[/tex] ------> is not true
therefore
the ordered pair is not a solution
case C) [tex](1,-3)[/tex]
Inequality A
[tex]-3<1-1[/tex]
[tex]-3<0[/tex] ------> is true
Inequality B
[tex]-3>-1+2[/tex]
[tex]-3>1[/tex] -------> is not true
therefore
the ordered pair is not a solution
case D) [tex](-2,3)[/tex]
Inequality A
[tex]3<-2-1[/tex]
[tex]3<-3[/tex] ------> is not true
therefore
the ordered pair is not a solution
