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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 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 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 to 3.

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

The graph represents the system of inequalities "4 x - y is less than or equal to 4 and 2 x - 2 y is less than or equal to 3" ⇒ 1.

Step-by-step explanation:

To find the answer let us find the equation of each line

Blue line:

∵ The line passes through points (1 , 0) and (0 , -4)

- Find the slope of the line

∵ m = Δy/Δx

∴

∴ m = 4

- The form of the equation is y = m x  + b, where b is the

   y-intercept (value y at x = 0)

∵ y = -4 at x = 0

∴ b = -4

- Write the equation of the line

∴ y = 4 x - 4

∴ The equation of the blue line is y = 4 x - 4

- The shading is above the line and the line is solid, that means

  y is greater than or equal 4 x - 4

∴ The inequality of the blue line is y ≥ 4 x - 4

Red line:

∵ The line passes through points (1.5 , 0) and (0 , -1.5)

- Find the slope of the line

∴

∴ m = 1

∵ y = -1.5 at x = 0

∴ b = -1.5

- Write the equation of the line

∴ y =  x - 1.5

- Multiply the both sides by 2

∴ The equation of the red line is 2 y = 2 x - 3

- The shading is above the line and the line is solid, that means

  y is greater than or equal 2 x - 3

∴ The inequality of the red line is 2 y ≥ 2 x - 3

Let us find which answer is the same with this system of inequalities

First

∵ 4 x - y ≤ 4

- Add y to both sides

∴ 4 x ≤ 4 + y

- Subtract 4 from both sides

∴ 4 x - 4 ≤ y

- That means 4 x - 4 is less than or equal y that means y

    is greater than or equal 4 x - 4

∴ y ≥ 4 x - 4 ⇒ same with first inequality above

∵ 2 x - 2 y ≤ 3

- Add 2 y to both sides

∴ 2 x ≤ 3 + 2 y

- Subtract 3 from both sides

∴ 2 x - 3 ≤ 2 y

- That means 2 x - 3 is less than or equal 2 y that means 2 y

    is greater than or equal 2 x - 3

∴ 2 y ≥ 2 x - 3 ⇒ same with second inequality above

The graph represents the system of inequalities "4 x - y is less than or equal to 4 and 2 x - 2 y is less than or equal to 3"

the correct is answer is a 9-sided polygon!