Select the correct answer from each drop-down menu.
2 answers:
Answer:
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 answer:
∵ 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"
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