Which statements are true about the graph of y ≤ 3x + 1 and y ≥ –x + 2? check all that apply. 1.the slope of one boundary line is 2.
2.both boundary lines are solid.
3.a solution to the system is (1, 3).
4.both inequalities are shaded below the boundary lines.
5.the boundary lines intersect.

2.Both boundary lines are solid.

3.A solution to the system is (1, 3)

5.The boundary lines intersect.

Step-by-step explanation:

we have

----> inequality A

The solution of the inequality A is the shaded area below the solid line

The slope of the solid line is 3

The point (1,3) is  a solution of inequality A (lie in the shaded area of the solution set)

----> inequality B

The solution of the inequality B is the shaded area above the solid line

The slope of the solid line is -1

The point (1,3) is a solution of inequality B (lie in the shaded area of the solution set)

The solution of the system of inequalities is the shaded area between the two solids lines

see the attached figure

Verify each statement

1.The slope of one boundary line is 2

The statement is False

2.Both boundary lines are solid.

The statement is True

3.A solution to the system is (1, 3)

The statement is True

4.Both inequalities are shaded below the boundary lines

The statement is False

5.The boundary lines intersect.

The statement is True

The intersection point is (0.25,1.75)

see the attached figure

The true statements are:

(2) Both boundary lines are solid.

(3)A solution to system is (1,3)

(5)The boundary line intersects.

Step-by-step explanation:

Given information:

The equation:

The solutions of the above inequalities is the bounded regions.

The first one will have the solution bounded region below the line and the second will have the solution bounded region above the line.

The slope of the line is 3

The slope of the line is -1

Now, check for the statements:

(A) The slope of the boundary line is 2

The statement is false.

(B) Both boundary lines are solid

The statement is true

(C) A solution of the system is(1,3)

The statement is true.

(D)Both inequalities are shaded below the boundary line.

The statement is false.

(E)The boundary line intersects.

The statement is true and the intersection points are (0.25,1.75)

(See attached figure)

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