How will the solution of the system y > 2x two-thirds and y < 2x one-third change if the inequality sign on both inequalities is reversed to y < 2x two-thirds and y > 2x one-third?

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11-05-2022
Mathematics

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How will the solution of the system y > 2x two-thirds and y < 2x one-third change if the inequality sign on both inequalities is reversed to y < 2x two-thirds and y > 2x one-third?

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MrRoyal MrRoyal · Answer 1 · 2022-05-16T11:44:10+02:00

Changing the inequality signs would ensure that the signs on the solution would also be reversed

How to determine the true statement?

The system of inequality is given as:

[tex]y > 2x + \frac 23[/tex]

[tex]y < 2x + \frac 13[/tex]

When the inequality signs are reversed, we have the following system of equations

[tex]y < 2x + \frac 23[/tex]

[tex]y > 2x + \frac 13[/tex]

Changing the inequality signs would ensure that the opposite region of the initial system of inequality is shaded, and the signs on the solution would also be reversed