SOLUTION: Graph the system of inequalities x<=2 y>=-2x+3

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Question 146396: Graph the system of inequalities

x<=2
y>=-2x+3
Answer by jim_thompson5910(35256) (Show Source):
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Jump to Inequality #1
Jump to Inequality #2
Jump to Solution

Inequality #1

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Start with the 1st inequality.

Replace the inequality sign with an equals sign.

So in order to graph , we need to graph first. So simply draw a vertical line through .

Graph of

Since the inequality sign is "<=", this tells us to shade to the left.

Graph of with the shaded region in green

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Now move onto the next inequality

Inequality #2

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Start with the 2nd inequality.

Replace the inequality sign with an equals sign.

So in order to plot , we need to plot the equation first.
(note: if you need help with graphing, check out this solver)

Graph of

Now plug in a test point (0,0) into the inequality

Start with the given inequality.

Plug in and

Evaluate and simplify.

Since the inequality is false, this means that we shade the entire region that does NOT contain the point (0,0)

In other words, we simply shade the entire region that is above the line.

Graph of with the shaded region in green

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Now draw all of the inequalities on the same coordinate system.
Graph of the 2 inequalities and their shaded regions.

The solution region will be the intersecting region of the inequalities.

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So the solution looks like:

Graph of the 2 lines and the final solution region represented by a series of dots.