On the set of axes, solve the following system of inequalities graphically.

Label the solution set S.

2x + 3y < - 3

y - 4x ≥ 2

2x + 3y < - 3 ⇒ 2x + 3y = - 3 ⇒ 2x + 3y = - 3

-4x + y ≥ 2 ⇒ - 4x + y = 2 ⇒ - 12x + 3y = 6

-14x = - 9

-14 - 14

x = ⁹/₁₄

2x + 3y = - 3

2 (⁹/₁₄) + 3y = - 3

1²/₇ + 3y = - 3

- 1²/₇ - 1²/₇

3y = - 4²/₇

3 3

y = - 1³/₇

The solution set is { (⁹/₁₄, - 1³/₇) }.