Question

identify the graph that represents the given system of inequalities. also, identify two ordered pairs that are solutions to the system. y ≤ x 5 y ≤ 2x 3

Answer 1

To identify the graph that represents the given system of inequalities y ≤ x + 5 and y ≤ 2x + 3, we can start by graphing each inequality separately and then shading the region that satisfies both inequalities. Two ordered pairs that are solutions to the system can be chosen from within the shaded region.

Step-by-step explanation:

The given system of inequalities is:

y ≤ x + 5

y ≤ 2x + 3

To identify the graph that represents this system, we can start by graphing the two inequalities separately.

Let's graph the inequality y ≤ x + 5 first:

- Start by graphing the line y = x + 5, which has a y-intercept of 5 and a slope of 1.

- Since we want to represent y ≤ x + 5, we need to shade the region that is below or on the line y = x + 5.

Now let's graph the inequality y ≤ 2x + 3:

- Graph the line y = 2x + 3, which has a y-intercept of 3 and a slope of 2.

- Shade the region that is below or on the line y = 2x + 3.

The graph that represents the given system of inequalities is the shaded region that is below or on both lines.

To find two ordered pairs that are solutions to the system, we can choose two points within the shaded region. For example, (0, 3) and (-2, 1) are two ordered pairs that are solutions to the system.

Answer 2

To identify the graph that represents the given system of inequalities, graph each inequality separately and find the overlapping region. Two ordered pairs that are solutions to the system are (0, 3) and (2, 7).

The system of inequalities y ≤ x + 5 and y ≤ 2x + 3 represents shaded areas below the lines y = x + 5 and y = 2x + 3, respectively.

The graph of the system would show the shaded region where both inequalities are simultaneously true, which is the area below both lines shaded in common.

Here are two ordered pairs that satisfy this system:

- For y ≤ x + 5 and y ≤ 2x + 3, one solution is the point of intersection between the lines y = x + 5 and y = 2x + 3.

- Solving x + 5 = 2x + 3:

x = 2

- Substituting x = 2 into y = x + 5:

y = 2 + 5 = 7

- So, one solution is (2, 7).

- Another point that satisfies both inequalities is a point in the shaded region below both lines, for instance, (0, 3), which lies in the shaded region where both y ≤ x + 5 and y ≤ 2x + 3 are true.

Question:

Identify the graph that represents the given system of inequalities. Also identify two ordered pairs that are solutions to the system.

y ≥ x + 5

y ≥ 2x + 3