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The graph of the given system of inequalities can be seen at the end of the answer.
<h3 /><h3>How to get the graph of the system of inequalities?</h3>Here we have the system of inequalities:
x + 3y > -3
y < 2x + 1
first, we can write both of these in the form of a line equation in the slope-intercept form.
y > (-3 - x)/3 = -1 - (1/3)*x
y < 2x + 1.
To graph this, we first need to draw the two lines as dashed lines (because the points on the lines are not solutions).
Then for the line:
y = -(1/3)*x - 1 we need to shade the region above the line (because the symbol > is used).
For the line:
y = 2x + 1
We need to shade the region below the line, because the symbol used is <.
Then the graph of the system of inequalities is the one you can see below. The solutions of the system are the ones where the two shaded regions intercept.
If you want to learn more about systems of inequalities:
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