2 Answers

Rahul Savani · Answer 1 · 2020-08-28T13:18:04+0000

Answer: THE GRAPH IS ATTACHED.

Explanation:

We know that the lines are:

x + 3y=-3

y = (1)/(2) x + 1

Solving for "y" from the first line, we get:

$3y=-x-3\\\\y=-(x)/(3)-1$

In order to graph them, we can find the x-intercepts and the y-intercepts.

For the line
x + 3y=-3 the x-intercepts is:

$0=-(x)/(3)-1\\\\(1)(-3)=x\\\\x=-3$

And the y-intercept is:

$y=-(0)/(3)-1\\\\y=-1$

For the line
y=(1)/(2) x + 1 the x-intercepts is:

$0=(1)/(2) x + 1\\\\-1(2)=x\\\\x=-2$

And the y-intercept is:

$y=(1)/(2) (0)+ 1\\\\y=1$

Now we can graph both lines, as you can observe in the image attached (The symbols
and
indicates that the lines must be dashed).

By definition, the solution is the intersection region of all the solutions in the system of inequalities.

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