Answer:
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
[tex]y\leq 3x+1[/tex] ----> inequality A
The solution of the inequality A is the shaded area below the solid line [tex]y=3x+1[/tex]
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)
[tex]y\geq -x+2[/tex] ----> inequality B
The solution of the inequality B is the shaded area above the solid line [tex]y=-x+2[/tex]
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:
[tex]y\leq 3x+1\\y\geq -x+2[/tex]
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 [tex]y\leq 3x+1[/tex] is 3
The slope of the line [tex]y\geq -x+2[/tex] 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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