Calculate the area of the domain in the xy-plane defined by the inequalities?

Question

Calculate the area of the domain in the xy-plane defined by the inequalities:

6x + 10y – 16 <= 0
-x + 10y + 26 >= 0
X >= - 4

The correct answer receives 10 points…. Urgent and more questions to follow up once this is solved

answer should be in area units

Answer 1

The three graphs form a triangle, so you need to find the 3 points of intersection:

6x + 10y = 16
-x + 10y = -26

Subtract second eq from the first:

7x = 42
x = 6, so -6 + 10y = -26, so y = -2. (6, -2)

The other 2 intersections are easier, just plug in x = -4:

6(-4) + 10y = 16
10y = 40
y = 4 (-4, 4)

-(-4) + 10y = -26
10y = -30
y = -3 (-4, -3)

So the length of the base of the triangle is 4 - (-3) = 7, and the height is the distance from the vertical line x = -4 to the intersection point (6, -2), or 6 - (-4) = 10.

So the area is 1/2(10)(7) = 35.

This is much easier to see if you draw it. (Sorry, I made a mistake the first time...I think this is right.)

Answer 2

Yeh answer is 40/3 or 13.33 sq units