How do I find a point of the vertices of three inequalities?

Question

y is greater than or equal to 3x-5

y is less or equal to -1/2 x +2

x is greater than or = to -4

choices

1. ( -4,20)

2.  ( -4,-15)

3. (-4,-4 )

4.( -4,4)

Answer 1

Given three inequlites are y ≥ 3x-5 , y ≤ -1/2 x+2 , x ≥ -4

Now we check if the each point is satisify the inequalities.

(-4,20)

20 ≥ -17 , 20 ≤ 4, -4 ≥ -4

It is not satisify the second inequlity.

(-4,-15)

-15 ≥ -17, -15 ≤ 4, -4 ≥ -4

It is satisify the three inequlites.

(-4,-4)

-4 ≥ -17, -4 ≤ 4, -4 ≥ -4

It is satisify the three inequlites.

(-4,4)

4 ≥ -17 , 4 ≤ 4, -4 ≥ -4

It is satisify the three inequlites.

(-4,-15),(-4,-4), (-4,4) are vertices of three inequalities.