Question

Which region represents the solution to the given system of inequalities?√y <-1/2 xly≥2x+3Bs4-5-4-3-7 -1C-2-3-5-DA23 4 5X

Answer 1

The given inequalities are

y < - x/2

y ≥2x + 3

We would select points from each region and input them into the inequalities.

For region A, (3, 3)

Substitute x = 3 and y = 3 into each inequality. We have

For

y < - x/2,

3 < - 3/2

This is not true

For region B, (- 3, 3)

Substitute x = - 3 and y = 3 into each inequality. We have

For

y < - x/2,

3 < - -3/2

3 < 3/2

This is not true

For region C, (- 4, - 2)

Substitute x = - 4 and y = - 2 into each inequality. We have

For

y < - x/2,

- 2 < - -4/2

- 2 < 2

This is true

For y ≥2x + 3

- 2 ≥ 2(- 4) + 3

- 2 ≥ - 8 + 3

- 2 ≥ - 5

This is also true

Since both inequalities are satisfied in region C,

the correct option is C