Question

A system of linear inequalities is shown above. ( in the picture )

Which of the following ordered pairs is a solution to the graph of the system of inequalities?

Select all that apply.

A. (-4,1)

B. (-3,-4)

C. (0, -3)

D. (0, 1)

E. (5,-2)

Answer 1

Answer:

C. (0, -3)

Step-by-step explanation:

The given system is

$- 2x - 3 \leqslant y$

$y - 1 \: < \: \frac{1}{2} x$

The point that satisfies both inequalities is the solution to the system.

When x=0 and y=-3.

We substitute into the first inequality to get:

$- 2(0) - 3 \leqslant - 3 \\ - 3 \leqslant - 3...true$

We again substitute into the second inequality to get:

$- 3- 1 \: < \: \frac{1}{2} (0) \\ - 4 \: < \: 0....true$

The point (0,-3) is a solution to the system of inequalities.