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)

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

2y - x ≥ -6

2(-1) - (-4) ≥ -6 {substituted into first inequality}

-2 + 4 ≥ -6 {multiplied}

2 ≥ -6 {added}

2y - 3x < -6

2(-1) - 3(-4) < -6 {substituted into second inequality}

-2 + 12 < -6 {multiplied}

10 < -6 {added}

2y - x ≥ -6

2(1) - 3 ≥ -6 {substituted into first inequality}

2 - 3 ≥ -6 {multiplied}

-1 ≥ -6 {subtracted}

2y - 3x < -6

2(1) - 3(3) < -6 {substituted into second inequality}

2 - 9 < -6 {multiplied}

-7 < -6 {subtracted}

__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*