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That is, we want to find the $(x,y)$ pairs that are solutions to both inequalities. First, we need to graph the lines $y=-2x-2$ and $y=-2$. Look at the grids to the left. On the left grid, you are looking at the graph of $y=-2x-2$. On the right, you are looking at the graph of $y=-2$.
Here is a way to see if the point $(1,2)$ is a solution to the first inequality:
$y≥-2x-2$ for $(1,2)$ ? $2≥-2(1)-2$ ? $2≥-2-2$ ? $2≥-4$ ? YES
Test each point in the table below in both inequalities. Also indicate which points are solutions to both.
Click on to see $y≥-2x-2$ and $y≥-2$ graphed together. The dark blue section is the area where the solution sets overlap. The light blue section is the rest of the solution set for $y≥-2$ and the pink section is the rest of the solution set for $y≥-2x-2$.
The red line is the graph of $y=-4x-2$ and the blue line is the graph of $3x+4y=18$.
For each point in the table below, locate the point on the grid and determine whether it is a solution to each inequality.
The graphs of the lines $x+y=-2$ and $2x-3y=6$ are given on the grid below. As you can see, the graphs of these two lines divide the grid into four sections, which have been labeled A, B, C, and D.
Choose a point in each section of the grid above (A, B, C, and D), and fill in the table below.