Which graph represents the solution set of the system of inequalities? −2x+y≤4 { y> x+2

Graph 2

Step-by-step explanation:

Given system of inequalities,

−2x + y ≤ 4,

y > x + 2

∵ Related equation of −2x + y ≤ 4 is,

-2x + y = 4 ⇒ y = 4 + 2x ----(1)

While, the related equation of y > x + 2 is,

y = x + 2

From equation (1),

4 + 2x = x + 2 ⇒ 4 + 2x - x = 2 ⇒ 4 + x = 2 ⇒ x = 2 - 4 ⇒ x = -2

Again by equation (1),

y = 4 + 2(-2) = 4 - 4 = 0

Hence, the intersection point of the related equation is (-2,0),

∴ Graph 1 and graph 3 can not be the graph of the given system.

Now, −2(0) + (0)  ≤ 4 ( true )

That is, −2x+y ≤ 4 would contain the origin,

Also, 0 > 0 + 2 ( False )

That is, y > x + 2 does not contain the origin.

Therefore, by the above explanation it is clear that,

Grap 2 represents the solution set of the system of inequalities.

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