Question

inequalities

Answer 1

where you given any directions?

Answer 2

Write a system of linear inequalities that describes the shaded region.
5x + 2y ? 30
x + 3y ? 15
x ? 0
y ? 0

Answer 3

We know that all the values we are looking at are in the first quadrant, which is always positive x and positive y, so that'd tell us the answer for the last two inequalities.

You can also see that the equations have clean intercepts (by the graph, they cross on specific points), so if we were to figure out the intercepts for each of the first two inequalities and distinguish which linr went with which inequality, we could test points on the shaded region to determine the correct relation.

Answer 4

Like, for example, the first inequality:
5x + 2y ? 30

We look at the specific line: 5x + 2y = 30
When y = 0, we have the x-intercept:
5x + 0 = 30
5x = 30
x = 6

When x = 0, we have the y-intercept
0 + 2y = 30
2y = 30
y = 15

So, we could test the point (0,0) (to shade that specific region shown, we are dealing with the graph below the line)

0 + 0 ? 30
0 ? 30
0 < 30
Well, 0 is < 30. So, the equation would be 5x + 2y <= 30 (<= is less-than-or-equal-to)