Question

Which graph represents the solution set of system of inequalities?

{ 3y>=x-9
{ 3x+y>-3

Answer 1

`3y\geqx-9\qquad|:3\\\\y\geq(1)/(3)x-3\\\\3x+y > -3\qquad|-3x\\\\y > -3x-3`

`\left\{\begin{array}{ccc}y\geq(1)/(3)x-3\\\\y > -3x-3\end{array}\right`

`y=(1)/(3)x-3\\\\for\ x=0\to y=(1)/(3)(0)-3=-3\to(0,\ -3)\\\\for\ x=3\to y=(1)/(3)(3)-3=1-3=-2\to(3,\ -2)\\\\y=-3x-3\\\\for\ x=0\to y=-3(0)-3=-3\to(0,\ -3)\\\\for\ x=-1\to y=-3(-1)-3=3-3=0\to(-1,\ 0)`

`y\geq(1)/(3)x-3`

solid line. we shade above the line

`y > -3x-3`

the dotted line. shadow above the line

Answer in the attachment (the first graph).

Answer 2

The first graph (picture of the graph attached)

Explanation:

We have two inequalities:

3y ≥ x-9

3x+y > -3

We have to see which graph represents the solution to these inequalities.

We are going to solve for some values of x:

First inequality 3y ≥ x-9

y ≥ (x-9) / 3

If we give values to x then we solve for y:

x y

-2 -3.67

0 -3

2 -2.34

4 1-67

With these values, we can graph the first line, which is continuous because the inequality has ≥

And because it is greater or equal to the shaded region is everything up from the line.

The second inequality 3x+y > -3

y > -3 - 3x

x y

-4 9

-2 3

0 -3

Now we can graph the second inequality which will be a continuous line because it only has >

The shaded region has to be up from the line because it is greater than.