Determine the solution to the system y≤2x-2 y≥-x-3
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To determine the solution to the system of inequalities, we need to find the region in the coordinate plane where the shaded areas of both inequalities overlap.
Let's start by graphing each inequality to understand their individual shading:
1) y ≤ 2x - 2:
We can start by drawing a straight line with a slope of 2 passing through the point (0, -2), and shade below the line, indicating that y is less than or equal to the given expression.
2) y ≥ -x - 3:
We can graph another straight line with a slope of -1 passing through the point (0, -3), and shade above the line to indicate that y is greater than or equal to the given expression.
Now, let's find the region where both shaded areas overlap. We are looking for the area that is shaded in both graphs.
The shaded region will be the solution to the system of inequalities.
It is difficult to draw a graph here, but if you have graph paper or a graphing tool, you can easily plot the lines and their respective shaded regions.
Once you have the graph, you can visually see the overlapping area, which is the solution to the system of inequalities.