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
∴ [tex]\frac{0-2.5}{5-0}=\frac{-2.5}{5}[/tex]
∴ 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
∴ [tex]m=\frac{-5-4}{3-0}=\frac{-9}{3}[/tex]
∴ 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
