Question

Which graph represents the solution set of the system of inequalities?

−2x+y≤4
{
y>x+2

Answer 1

Graph 2

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.

Answer 2

Look at the given equations : -2x + y ≤ 4 & y > x + 2

For equation -2x + y = 4,
Solutions are (0, 4), (-2, 0)

For equation y = x + 2,
Solutions are (-2, 0), (0, 2)

Graph second & Third obey this solution,

Take a point (5, 0) and put into the equations,
It does not obey both the equations,

So, Graph second is the correct answer.