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Graph the solution to the following system of inequalities.y>3x+7y≤−3x-8

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Step 1. Graphing the first inequality.

The first inequality is:


y>3x+7

to graph this, we need to graph the line 3x+7, which compared with the slope-intercept equation


y=mx+b

where m is the slope and b is the y-intercept, the line


y=3x+7

is a line with a slope of 3 and a y-intercept at 7:

SInce the inequality is:


y>3x+7

The solution just for this inequality are the values greater than the red line, but not including the red line so we represent is a dotted line and a shaded part above:

Step 2. Graph the second inequality.

The second inequality is:


y\le-3x-8

As we did with the first inequality, we graph the line -3x-8 first.

comparing -3x-8 with the slope-intercept equation:


y=mx+b
y=-3x-8

we can see that the slope m is -3 and the y-intercept b is -8. This line is shown in blue in the following diagram along with our results for the previous inequality:

Since the inequality form is:


y\le-3x-8

We shade the values below this blue line:

The final solution will be the intersection between the red part and the blue part:

Graph the solution to the following system of inequalities.y>3x+7y≤−3x-8-example-1
Graph the solution to the following system of inequalities.y>3x+7y≤−3x-8-example-2
Graph the solution to the following system of inequalities.y>3x+7y≤−3x-8-example-3
Graph the solution to the following system of inequalities.y>3x+7y≤−3x-8-example-4
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