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Graphical representation of a first degree inequality with two variables


Practical method

  • We replaced inequality with equality.

  • We draw the line on the Cartesian plane.

  • We choose an auxiliary point, preferably point (0, 0), and verify whether or not it satisfies the initial inequality.

If so, the inequality solution corresponds to the semiplane to which the auxiliary point belongs.

If not, the inequality solution corresponds to the opposite semiplane to which the auxiliary point belongs. Example:

  • Let's graph the inequality

    Table:

    x

    y

    (x, y)

    04(0, 4)
    20(2, 0)

    Graphic:

Replacing the auxiliary point (0, 0) in the inequality, we verify:

(Positive affirmative, the auxiliary point satisfy the inequality)

The inequality solution corresponds to the semiplane to which the auxiliary point belongs (0, 0).

Next: Graphical Resolution of an Inequality System