Answer:
The system of inequality that has a solution set that is a line is:
[tex]x+y\geq 3\\\\x+y\leq 3[/tex]
Step-by-step explanation:
We know that if:
[tex]a\leq b[/tex]
and
[tex]a\geq b[/tex]
Then the resulting equation from both the inequalities is:
a=b
Hence, from the option (A) we have:
[tex]x+y\geq 3--------(1)[/tex]
and [tex]x+y\leq 3-------------(2)[/tex]
Hence, the equation that is resulting from the above system of inequalities is:
[tex]x+y=3[/tex]
( Since, the inequality (1) is a solid straight line passing through the point (0,3) and (3,0) and the shaded region is away from the origin, above the line.
and from inequality (2) we get a solid straight line passing through the point (0,3) and (3,0) and the shaded region is towards the origin, below the line )
Hence, the common region that satisfy from both the inequality is a line:
[tex]x+y=3[/tex]
