SOLUTION: Find the coordinates of the vertices of the figure formed by each system of inequalities. y≥−2 2x+y≤2 y≤2x+6

Algebra ->  Graphs -> SOLUTION: Find the coordinates of the vertices of the figure formed by each system of inequalities. y≥−2 2x+y≤2 y≤2x+6      Log On


   



Question 1153788: Find the coordinates of the vertices of the figure formed by each system of inequalities.
y≥−2
2x+y≤2
y≤2x+6

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
first graph given lines (as equalities )
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C-2+%2C-2%2C2x%2B6%2C2-2x%29+
he figure formed by each system is a triangle and you can find the coordinates of the vertices so that you find intersection points of the all three lines
given:
y%3E=-2.......1)-> horizontal line
2x%2By%3C=2.......2)
y%3C=2x%2B6.......3)
---------------------------
y%3E=-2.......1)...........substitute in 2)
2x-2%3C=2.......2)
2x%3C=2%2B2
2x%3C=4
x%3C=2+
intersection point of the lines 1) and 2) is at (2,-2)
y%3E=-2.......1)...........substitute in 3)
-2%3C=2x%2B6.......3)
-2-6%3C=2x
-8%3C=2x
-4%3C=x

intersection point of the lines 1) and 3) is at (-4,-2)

2x%2By%3C=2.......2)......solve for y
y%3C=2-2x.......2).........substitute in 3)
2-2x%3C=2x%2B6.......3).....solve for x
2-6%3C=2x%2B2x
-4%3C=4x
-1%3C=x
then
y%3C=2-2%28-1%29
y%3C=2%2B2
y%3C=4
intersection point of the lines 2) and 3) is at (-1,4)
now, plot these points: