Question

Which system of inequalities is represented by the graph?

Answer 1

Answer:

The system of inequalities " x + 2 y ≤ 5 and 3 x + y ≤ 4 " is represented by the graph ⇒ D

Step-by-step explanation:

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

Blue line:

∵ The line passes through points (5 , 0) and (0 , 2.5)

- Find the slope of the line

∵ m = Δy/Δx

∴ $\frac{0-2.5}{5-0}=\frac{-2.5}{5}$

∴ m = -0.5

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

   y-intercept (value y at x = 0)

∵ y = 2.5 at x = 0

∴ b = 2.5

- Write the equation of the line

∴ y = - 0.5 x + 2.5

- Multiply both sides by 2

∴ The equation of the blue line is 2 y = - x + 5

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

  2 y is less than or equal - x + 5

∴ The inequality of the blue line is 2 y ≤ - x + 5

Red line:

∵ The line passes through points (3 , -5) and (0 , 4)

- Find the slope of the line

∴ $m=\frac{-5-4}{3-0}=\frac{-9}{3}$

∴ m = -3

∵ y = 4 at x = 0

∴ b = 4

- Write the equation of the line

∴ y =  -3 x + 4

∴ The equation of the red line is y = -3 x + 4

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

  y is less than or equal -3 x + 4

∴ The inequality of the red line is y ≤ -3 x + 4

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

∵ 2 y ≤ - x + 5

- Add x to both sides

∴ x + 2 y ≤ 5 ⇒ same as the first inequality of answer D

∵ y ≤ -3 x + 4

- Add 3 x to both sides

∴ 3 x + y ≤ 4 ⇒ same as the second inequality of answer D

The system of inequalities " x + 2 y ≤ 5 and 3 x + y ≤ 4" is represented by the graph