Answer: THE GRAPH IS ATTACHED.
Step-by-step explanation:
We know that the lines are:
[tex]x + 3y=-3[/tex]
[tex]y = \frac{1}{2} x + 1[/tex]
Solving for "y" from the first line, we get:
[tex]3y=-x-3\\\\y=-\frac{x}{3}-1[/tex]
In order to graph them, we can find the x-intercepts and the y-intercepts.
For the line [tex]x + 3y=-3[/tex] the x-intercepts is:
[tex]0=-\frac{x}{3}-1\\\\(1)(-3)=x\\\\x=-3[/tex]
And the y-intercept is:
[tex]y=-\frac{0}{3}-1\\\\y=-1[/tex]
For the line [tex]y=\frac{1}{2} x + 1[/tex] the x-intercepts is:
[tex]0=\frac{1}{2} x + 1\\\\-1(2)=x\\\\x=-2[/tex]
And the y-intercept is:
[tex]y=\frac{1}{2} (0)+ 1\\\\y=1[/tex]
Now we can graph both lines, as you can observe in the image attached (The symbols [tex]<[/tex] and [tex]>[/tex] indicates that the lines must be dashed).
By definition, the solution is the intersection region of all the solutions in the system of inequalities.
