Question

If you graph the system of inequalities given below, which points would lie in the solution set? Select all the correct answers.

Answer 1

Answer:

Option b and e.

Step-by-step explanation:

Given : If you graph the system of inequalities

$x -y \geq -4\\2x- y \leq5\\2y + x > 1$

To find : Which points would lie in the solution set?

Solution :

The point that lie in the solution set will satisfy all three inequalities.

First we plot the graph of the given inequalities.

$x -y \geq -4\\2x- y \leq 5\\2y + x > 1$

Refer the attached figure below.

The shaded region in the graph is the required area under the given equation.

We mark all the points on the graph and have seen that (3,5) and (-1,3) point lie inside and on the shaded region respectively.

Verification by putting the point in the inequalities,

Equation 1 - $x -y \geq -4$

$3 -5\geq -4$

$-2\geq -4$ satisfy.

Equation 2 - $2x- y \leq5$

$2(3) -5 \leq5$

$1\leq 5$ satisfy.

Equation 3 - $2y + x > 1$

$2(5) + 3 > 1$

$13>1$ satisfy.

Similarly point (-1,3) also satisfy all the equation and lie on the solution set.

Therefore, Option b and e are correct.

Answer 2

Its just a matter of subbing...but keep in mind, for it to be a solution, it has to satisfy all 3 inequalities

x - y > = -4
2x - y < = 5
2y + x > 1

solutions are : (-1,3) and (3,5)