Question

Which system of inequalities does the graph represent? Which test point satisfies both of the inequalities in that system?

The graph represents the system of inequalities .

The test point satisfies both of the inequalities in the system represented by the graph.

Graph represents: 1. 4x - y is less than or equal to 4 and 2x - 2y is less than or equal to 3. 2. 4x - y is greater than or equal to 4 and and 2x - 2y is less than or equal to 3. 3. 4x - y is less than or equal to 4 and 2x - 2y is greater than or equal to 3. 4. 4x - y is greater than or equal to 4 and 2x - 2y is greater than or equal

Answer 1

1. 4x - y is less than or equal to 4 and 2x - 2y is less than or equal to 3

Explanation:

Blue line:

y > 4x - 4

y - 4x > -4

4x - y < 4

Test point: (0,0)

4(0) - 0 = 0 < 4

Red line:

y > x - 1.5

2y > 2x - 3

2x - 2y < 3

Test point: (0,0)

2(0) - 2(0) = 0 < 3

Answer 2

The graph represents the system of inequalities 4x - y <= 4 and 2x - 2y <= 3. The test point (0, 0) satisfies both of the inequalities in that system.

The graph represents the system of inequalities:

4x - y ≤ 4

2x - 2y ≤ 3

The test point (0, 0) satisfies both of the inequalities in the system.

To see why, we can substitute (0, 0) into each inequality.

For the first inequality, we get:

4(0) - 0 ≤ 4

0 ≤ 4

This is true.

For the second inequality, we get:

2(0) - 2(0) ≤ 3

0 ≤ 3

This is also true.

Therefore, the test point (0, 0) satisfies both of the inequalities in the system, and the graph represents the system of inequalities:

4x - y ≤ 4

2x - 2y ≤ 3