Find the coordinates of the vertices formed by the system of inequalities. x + y ≤ 9 y ­- 2x ≥ -21 y ≥ -4x + 15 A (­6, ­-9), (10, ­-1), (2, 7)B (­-9,- ­6), (-­1, 10), (7, 2) C (­-30, ­-21), (­-6, -9), (6, 15) D (­-6, ­-9), (6, ­-3), (-­12, ­-21)

Answer:AStep-by-step explanation:To find the coordinates of the vertices , treat the inequalities as equations and solve them in pairs, simultaneously, that isx + y = 9 → (1)y - 2x = - 21 → (2) ← add 2x to both sidesy = - 21 + 2x → (3)Substitute y = - 21 + 2x into (1)x - 21 + 2x = 93x - 21 = 9 ( add 21 to both sides )3x = 30 ( divide both sides by 3 )x = 10Substitute x = 10 into (3)y = - 21 + 20 = - 1Coordinates of vertex = (10, - 1 )---------------------------------------------------------------------y - 2x = - 21 → (1)y = - 4x + 15 → (2)Substitute y = - 4x + 15 into (1)- 4x + 15 - 2x = - 21- 6x + 15 = - 21 ( subtract 15 from both sides )- 6x = - 36 ( divide both sides by - 6 )x = 6Substitute x = 6 into (2)y = - 24 + 15 = - 9Coordinates of vertex = (6, - 9 )------------------------------------------------------------------------x + y = 9 → (1)y = - 4x + 15 → (2)Substitute y = - 4x + 15 into (1)x - 4x + 15 = 9- 3x + 15 = 9 ( subtract 15 from both sides )- 3x = - 6 ( divide both sides by - 3 )x = 2Substitute x = 2 into (2)y = - 8 + 15 = 7Coordinates of vertex = (2, 7 )