The solution to the following system of inequalities is option D.
How to estimate the system of inequalities?
There exist two inequalities drawn on a graph.
x + 2y ≤ 4 .............(1)
3x - y ≤ 2 .............(2)
Here solution set of the inequality (1) will be described by the shaded area below the solid line (in blue) characterized by "x + 2y = 4".
⇒ x + 2y < 4
⇒ x + 2y = 4
⇒ 2+ 2(0) = 2
⇒ 2< 4 (true)
(Line x + 2y = 4 will have the slope slanting down and y-intercept as 2)
Second inequality will designate the shaded area on the left of the solid red line characterized by "3x - y ≤ 2".
⇒ 3x – y > 2
⇒ 3(2)-0= 6
⇒ 6>2 (true)
(Line 3x - y = 2 will have the slope upwards and y-intercept as -2)
The solution area to these inequalities will be the common area shaded in green.
Therefore, the correct answer is option D.
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