Which point lies on the solution set for the system of inequalities?

Which point lies on the solution set for the system?
2y - x ≥ -6
2y - 3x < -6

A.)  (-4,-1)
B.)  (3,1)
C.)  (0,-3)
D.)  (4,3)

Substitute the coordinates, from the answer choices, into the inequalities.  If it creates a true statement, in both inequalities, then that point lies on the solution set for the system.

For point A.)  (-4,-1)
2y - x ≥ -6
2(-1) - (-4) ≥ -6   {substituted into first inequality}
-2 + 4 ≥ -6   {multiplied}
2 ≥ -6   {added}
True statement

2y - 3x < -6
2(-1) - 3(-4) < -6   {substituted into second inequality}
-2 + 12 < -6   {multiplied}
10 < -6   {added}
False statement.  Point A.) does not lie on the solution set.

For point B.)  (3,1)
2y - x ≥ -6
2(1) - 3 ≥ -6   {substituted into first inequality}
2 - 3 ≥ -6   {multiplied}
-1 ≥ -6   {subtracted}
True statement.

2y - 3x < -6
2(1) - 3(3) < -6   {substituted into second inequality}
2 - 9 < -6   {multiplied}
-7 < -6   {subtracted}
True statement.   Point B.)  does lie on the solution set.

B.)  (3,1)

- Algebra House