Question

Which is the graph of the system x + 3y > –3 and y < One-halfx + 1?

Answer 1

Answer:

The Last Graph is the answer

Answer 2

Answer: THE GRAPH IS ATTACHED.

Step-by-step explanation:

We know that the lines are:

$x + 3y=-3$

$y = \frac{1}{2} x + 1$

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

$3y=-x-3\\\\y=-\frac{x}{3}-1$

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:

$0=-\frac{x}{3}-1\\\\(1)(-3)=x\\\\x=-3$

And the y-intercept is:

$y=-\frac{0}{3}-1\\\\y=-1$

For the line $y=\frac{1}{2} x + 1$ the x-intercepts is:

$0=\frac{1}{2} x + 1\\\\-1(2)=x\\\\x=-2$

And the y-intercept is:

$y=\frac{1}{2} (0)+ 1\\\\y=1$

 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.