Answer:
The graph shows the solution to the system inequalities
y ≥ -3x + 3 and y ≥ 2x ⇒ answer D
Step-by-step explanation:
* Lets study the graph to solve the question
- There are two solid lines, that means the sign of the inequalities
are ≤ or ≥
- One of the two line passes through the origin and the other
intersect the y-axis
- The shaded region is over the two lines, then the signs of the
inequalities are ≥ (greater than or equal)
* Lets make the equations of the two lines
∵ The form of the equation is y = mx + c, where m is the slope of the
line and c is the y-intercept
- The rule of the slope of the line wich passes through points (x1 , y1)
and (x2 , y2) is m = (y2 - y1)/(x2 - x1)
- Y-intercept means the line intersect the y-axis at point (0 , c)
* Now lets find from the graph two points on each line to make the
equations of the lines
# The line which passes through the origin
∵ Points (0 , 0) and (5 , 10) are on the line
- Let (0 , 0) is (x1 , y1) and (5 , 10) is (x2 , y2)
∴ m = (10 - 0)/(5 - 0) = 10/5 = 2
∴ The equation of the line is y = 2x + c
∵ The line passes through the origin
∴ c = 0
∴ The equation of the line is y = 2x
- The shaded is over the line
∴ The inequality is y ≥ 2x
# The line which intersect the y-axis at point (0 , 3)
∵ Points (0 , 3) and (1 , 0) are on the line
- Let (0 , 3) is (x1 , y1) and (1 , 0) is (x2 , y2)
∴ m = (0 - 3)/(1 - 0) = -3/1 = -3
∴ The equation of the line is y = -3x + c
∵ The line passes through the point (0 , 3)
∴ c = 3
∴ The equation of the line is y = -3x + 3
- The shaded is over the line
∴ The inequality is y ≥ -3x + 3
∴ The graph shows the solution to the system inequalities :
y ≥ -3x + 3 and y ≥ 2x
