Question

Graph the solution of the system of linear inequalities. Please use plots on my graph. y ≤-2x-2y ≥x+2

Answer 1

We have a system of inequalities:

`\begin{gathered} y\le-2x-2 \\ y\ge x+2 \end{gathered}`

The solution will be a region in which both inequalities are satisfied.

To solve this we start by graphing the equalities within the inequalities. This means the lines that limit the region where the inequality is true from the region where the inequality is false.

In this case, this lines are:

`\begin{gathered} y=-2x-2 \\ y=x+2 \end{gathered}`

They are simply the lines where y is not greater or smaller than an expression but equal to that expression.

We then can plot them in the graph as:

Now, we can convert each of the lines in boundaries for a region by looking at each inequality.

The first inequality, y ≤-2x-2, tells us that the valid region for y is below the red line (including the values in the line).

The second inequality, y ≥x+2, tells us that the valid region for y is above the blue line, including the values in the line.

Then, we should find a region for y where it is above the blue line and below the red line at the same time.

This region is the green region: