Question

Which region represents the solution to the given system of inequalities?

Answer 1

Answer: The intersection region shown in the graph attached is the solution of the system of inequalities.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

 Given the following system of inequalities:

$\left \{ {{x+3y\leq-3 } \atop {x\geq3 }} \right.$

We need to graph the lines.

We have the line:

$x+3y=-3$

Solving for "y", we get:

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

Knowing that $m=-\frac{1}{3}$ and $b=-1$, we can graph it.

Since the symbol is $\leq$, the line must be solid.

The other line is:

$x=3$

Since "x" only takes one value, we can identify that it is a vertical line, so we can graph it.

Since the symbol is $\geq$, the line must be solid.

We need to substitute a point that is not on the line, into each inequalities. Let's choose the point (0,0).

Then:

$0+3(0)\leq-3\\\\0\leq-3$

This is false, therefore, we must shade the half that does not contain this point.

$0\geq 3$

This is false, so we must shade the half that does not contain this point.

The intersection region of the solutions (Observe the graph attached) of the given inequalities is the solution of the system of inequalities.

Answer 2

Answer:

a

Step-by-step explanation: