Question

Can u please tell me The coordinates on where to plot them to!

Answer 1

`\begin{gathered} \text{Given} \\ -2x-y\geq2 \\ y\geq-2 \\ x\ge-2 \end{gathered}`

Graphing -2x - y ≥ 2.

First, rearrange the inequality so that only y is in the left side.

`\begin{gathered} -2x-y\geq2 \\ -y\ge2x+2 \\ (-y)/(-1)\ge(2x+2)/(-1),\text{ divide both sides by }-1\text{ to get rid of }y\text{'s negative} \\ \text{Dividing negative both sides also flips the inequality.} \\ y\le-2x-2 \end{gathered}`

Next, choose two, and substitute any values for x. In this case we will use x = 0, and x = -1.

`\begin{gathered} \text{If }x=0 \\ y\le-2x-2 \\ y\le-2(0)-2 \\ y\le-2 \\ \text{Plot point }(0,-2)\text{ on the graph} \\ \\ \text{If }x=-1 \\ y\le-2(-1)-2 \\ y\le2-2 \\ y\le0 \\ \text{Plot point }(-1,0)\text{ on the graph.} \end{gathered}`

Once you have plotted (0, -2) and (-1,0) on the graph, draw a solid line between the two points.

Since the inequality of the rearranged equation is less than or equal ( ≤ ), then shade the lower area of the line.

Graphing y ≥ -2.

Draw a horizontal line at y = -2, and stack it in the existing graph. The inequality sign is greater than or equal to ( ≥ ), then shade the upper area of the line.

Graphing x ≥ -2.

Draw a vertical line at x = -2, and stack it on the existing graph. The inequality sign is greater than or equal to ( ≥ ). Then we shade the right area of the line. The graph below represents the final output when we graph all the three systems of inequality.

The shaded area is necessary since they represent the inequality, however without the inequality sign, the line of the graphs would look like this.