Question

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

Label the solution set S.
2x + 3y < -3
y - 4x ≥ 2

Answer 1

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)}.