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

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

System

using a graph tool

the solution is the line

see the attached figure N

System

using a graph tool

the solution is the shaded area

see the attached figure N

System

using a graph tool

The system has no solution

see the attached figure N

System

using a graph tool

the solution is the shaded area

see the attached figure N

therefore

the answer is

System

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

Step-by-step explanation:

We know that if:

and

Then the resulting equation from both the inequalities is:

                               a=b

Hence, from the option (A) we have:

and

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

( 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:

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1