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Question

Identify the vertex of the system of inequalities.

  

Answer 1

Let find equatios of these lenes by identifying 2 points.

On first line we see (-4,4) and (0,6). Then slope m₁= (6-4)/(0-(-4)= 1/2. Equation of first line y = 1/2x + 6

On second line we see points (-8, 4) and (-12, 6). Then slope m₂ = (6-4)/(-12 + 8) = -1/2.

Then equation of second line is y - 4 = -1/2(x +8), y = -1/2x.

Vertex of solution region is intersection point of this lines. We have system

y = 1/2x + 6

y =-1/2x

1/2x +6 = -1/2x, x= - 6and y = 3

Answer: (-6,3) is vertex of solution region

Answer 2

the vertex is where the lines intersect, at (-6,3)