we're proceeding to verify each case
we have
[tex]y < 3x-1[/tex] ------> inequality A
[tex]y\geq -x+4[/tex] -----> inequality B
Case A) point [tex](4,0)[/tex]
[tex]x=4\\y=0[/tex]
Verify Inequality A
[tex]y < 3x-1[/tex]
[tex]0 < 3*4-1[/tex]
[tex]0 < 11[/tex] ------> is true
Verify Inequality B
[tex]y\geq -x+4[/tex]
[tex]0\geq -4+4[/tex]
[tex]0\geq 0[/tex] -------> is true
therefore
the point [tex](4,0)[/tex] is a solution
Case B) point [tex](1,2)[/tex]
[tex]x=1\\y=2[/tex]
Verify Inequality A
[tex]y < 3x-1[/tex]
[tex]2 < 3*1-1[/tex]
[tex]2 < 2[/tex] ------> is not true
Verify Inequality B
[tex]y\geq -x+4[/tex]
[tex]2\geq -1+4[/tex]
[tex]2\geq 3[/tex] -------> is not true
therefore
the point [tex](1,2)[/tex] is not the solution
Case C) point [tex](0,4)[/tex]
[tex]x=0\\y=4[/tex]
Verify Inequality A
[tex]y < 3x-1[/tex]
[tex]4 < 3*0-1[/tex]
[tex]4 < -1[/tex] ------> is not true
Verify Inequality B
[tex]y\geq -x+4[/tex]
[tex]4\geq -0+4[/tex]
[tex]4\geq 4[/tex] -------> is true
therefore
the point [tex](0,4)[/tex] is not the solution
Case D) point [tex](2,1)[/tex]
[tex]x=2\\y=1[/tex]
Verify Inequality A
[tex]y < 3x-1[/tex]
[tex]1 < 3*2-1[/tex]
[tex]1 < 5[/tex] ------> is true
Verify Inequality B
[tex]y\geq -x+4[/tex]
[tex]1\geq -2+4[/tex]
[tex]1\geq2[/tex] -------> is not true
therefore
the point [tex](2,1)[/tex] is not the solution
therefore
the answer is
[tex](4,0)[/tex]
Answer:
The answer is A
Step-by-step explanation:
I took the test
