SOLUTION: Find the coordinates of the vertices of the figure formed by the system of inequalities x + y ≤ 2 x - 2y ≤ 8 x + (-1/3)y ≥ -2/3

Algebra ->  Graphs -> SOLUTION: Find the coordinates of the vertices of the figure formed by the system of inequalities x + y ≤ 2 x - 2y ≤ 8 x + (-1/3)y ≥ -2/3       Log On


   

Question 1049501: Find the coordinates of the vertices of the figure formed by the system of inequalities
x + y ≤ 2
x - 2y ≤ 8
x + (-1/3)y ≥ -2/3
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the coordinates of the vertices of the figure formed by the system of inequalities
1st:: x + y ≤ 2
2nd:: x - 2y ≤ 8
3rd:: x + (-1/3)y ≥ -2/3
------
1st:: y <= -x+2
2nd: y >= (x-8)/2
3rd:: y <= (x+(2/3))/(1/3)
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Intersection of 1st and 2nd::
-x+2 = (x/2) - 4
(3/2)x = 6
x = 4
y = -x+2 = -2
Vertex:: (4,-2)
-----------------
Intersection of 1st and 3rd::
-x+2 = 3x + 2
4x = 0
x = 0
y = -x+2 = 2
Vertex:: (0,2)
----
Intersection of 2nd and 3rd::
(x/2)-4 = 3x+2
(5/2)x = -6
x = -12/5 = -(2 2/5)
y = 3x+2 = 3(-12/5)+(10/5) = -26/5 = -(5 1/5)
Vertex:: (-12/5,-26/5)
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Cheers,
Stan H.
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