Answer:
Graph D
Step-by-step explanation:
We are given that system of inequalities
[tex]x+3y>6[/tex]....(1)
[tex]y\geq 2x+4[/tex]...(2)
The two equations can be written as
[tex]x+3y=6[/tex]...(3)
[tex]y=2x+4[/tex]...(4)
Substitute x=0 in equation (3)
[tex]3y=6[/tex]
[tex]y=2[/tex]
Substitute y=0
[tex]x=6[/tex]
The equation x+3y=6 is passing through the points (0,2) and (6,0).
Substitute x=0 and y=0 in equation (1) then , we get
[tex]0>6[/tex]
It is not true therefore, shaded region above the line.
Substitute x=0 in equation (4)
[tex]y=4[/tex]
Substitute y=0
[tex]2x=-4[/tex]
[tex]x=-2[/tex]
The equation y=2x+4 is passing through the points (0,4) and (-2,0).
Substitute x=0 and y=0 in equation (2)
[tex]0\geq 4[/tex]
It is not true therefore, shaded region above the line.
[tex]x=6-3y[/tex]
Substitute the value of x in equation (4)
[tex]y=2(6-3y)+4[/tex]
[tex]y=12-6y+4[/tex]
[tex]y+6y=16[/tex]
[tex]7y=16[/tex]
[tex]y=\frac{16}{7}=2.29[/tex]
Substitute [tex]y=\frac{16}{7}[/tex] in equation (3)
[tex]x+\frac{48}{7}=6[/tex]
[tex]x=6-\frac{48}{7}=\frac{42-48}{7}=-\frac{6}{7}[/tex]
[tex]x=-0.86[/tex]
The two equations intersect to each other at point (-0.86,2.29).
The common region between two equations is in blue colour.
It is solution of two inequalities equations.
Hence, graph D is true.
