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