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How will the solution of the system y>2x+2/3 and y<2x1/3 change if the inequality sign on both inequalities is reversed

Sagot :

facundo3141592

Answer:

We have the inequalities:

y > 2*x + 2/3

y < 2*x + 1/3

First, we need to understand how to see the solutions of each one of these.

y > 2*x + 2/3

The solution set of this inequality will be ALL the points above the line:

y = 2*x + 2/3

And the solution of the inequality:

y < 2*x + 1/3

Will be the set of all the points below the line:

y = 2*x + 1/3

Notice that line "y = 2*x + 2/3" is above than the line "y = 2*x + 1/3"

Then the system:

y > 2*x + 2/3

y < 2*x + 1/3

Has no solutions.

If we reverse both inequalities, we will get:

y < 2*x + 2/3

y > 2*x + 1/3

Now the solution of the first inequality will be all of the region below the line, and the solution for the second will be all the region above the line.

In this case, the solution of the system will be all the region between both lines, as we can see on the graph below. Where the solution of the system is the doubled shaded area.

View image facundo3141592
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