Question

Which system of inequalities has a solution set that is a line?

Answer 1

We're going to solve each of the systems to determine the solution.

System $1$

$x+y \geq 3\\ x+y \leq 3$

using a graph tool

the solution is the line $x+y=3$

see the attached figure N $1$

System $2$

$x+y \geq -3\\ x+y \leq 3$

using a graph tool

the solution is the shaded area

see the attached figure N $2$

System $3$

$x+y > 3\\ x+y < 3$

using a graph tool

The system has no solution

see the attached figure N $3$

System $4$

$x+y > -3\\ x+y < 3$

using a graph tool

the solution is the shaded area

see the attached figure N $4$

therefore

the answer is

System $1$

$x+y \geq 3\\ x+y \leq 3$

Answer 2

Answer:

The system of inequality that has a solution set that is a line is:

$x+y\geq 3\\\\x+y\leq 3$

Step-by-step explanation:

We know that if:

$a\leq b$

and

$a\geq b$

Then the resulting equation from both the inequalities is:

                               a=b

Hence, from the option (A) we have:

$x+y\geq 3--------(1)$

and $x+y\leq 3-------------(2)$

Hence, the equation that is resulting from the above system of inequalities is:

$x+y=3$

( 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:

              $x+y=3$