QUESTION 1
The given inequality is
[tex]y\leq x-3[/tex] and [tex]y\geq -x-2[/tex].
If (3,-2) is a solution; then it must satisfy both inequalities.
We put x=3 and y=-2 in to both inequalities.
[tex]-2\leq 3-3[/tex] and [tex]-2\geq -3-2[/tex].
[tex]-2\leq 0[/tex]:True and [tex]-2\geq -5[/tex]:True
Both inequalities are satisfied, hence (3,-2) is a solution to the given system of inequality.
QUESTION 2
The given inequality is
[tex]y\:>\:-3x+3[/tex] and [tex]y\:>\: x+2[/tex].
If (1,4) is a solution; then it must satisfy both inequalities.
We put x=1 and y=4 in to both inequalities.
[tex]4\:>\:-3(1)+3[/tex] and [tex]4\:>\: 1+2[/tex].
[tex]4\:>\:0[/tex]:True and [tex]4\:>\: 3[/tex]:True
Both inequalities are satisfied, hence (1,4) is a solution to the given system of inequality.
Ans: True
QUESTION 3
The given inequality is
[tex]y\leq 3x-6[/tex] and [tex]y\:>\: -4x+2[/tex].
If (0,-2) is a solution; then it must satisfy both inequalities.
We put x=0 and y=-2 in to both inequalities.
[tex]-2\leq 3(0)-6[/tex] and [tex]-2\:>\: -4(0)+2[/tex].
[tex]-2\leq -6[/tex]:False and [tex]-2\:>\:2[/tex]:False
Both inequalities are not satisfied, hence (0,-2) is a solution to the given system of inequality.
Ans:False
QUESTION 4
The given inequality is
[tex]2x-y\:<\: 4[/tex] and [tex]x+y\:>\:-1[/tex].
If (0,3) is a solution; then it must satisfy both inequalities.
We put x=0 and y=3 in to both inequalities.
[tex]2(0)-3\:<\: 4[/tex] and [tex]0+3\:>\:-1[/tex].
[tex]-3\:<\: 4[/tex]:True and [tex]3\:>\:-1[/tex]: True
Both inequalities are satisfied, hence (0,3) is a solution to the given system of inequality.
Ans:True
QUESTION 5
The given system of inequality is
[tex]y\:>\:2x-3[/tex] and [tex]y\:<\:x+6[/tex].
If (-3,0) is a solution; then it must satisfy both inequalities.
We put x=-3 and y=0 in to both inequalities.
[tex]0\:>\:2(-3)-3[/tex] and [tex]0\:<\:-3+6[/tex].
[tex]0\:>\:-9[/tex];True and [tex]0\:<\:3[/tex]:True
Both inequalities are satisfied, hence (-3,0) is a solution to the given system of inequality.
Ans:True
