Question

The solution set of the inequation $2x + y > 5$ is
A. Half plane that contains the origin
B. Open half plane not containing the origin
C. Whole $y -$ plane except the points lying on the line $2x + y = 5$
D. None of the above

Answer 1

Would start solving by putting the given conditions in the equation according to the given possible options given in the question.

Complete step by step solution:
Given that: $2x + y > 5$
Verifying the possibility of option A: Half plane that contains the origin
On putting $x = 0,y = 0$ in the given condition
$\begin{array}{l} \Rightarrow 2(0) + 0 > 5\\\ \Rightarrow 0 > 5 \end{array}$
Zero greater than five is not possible. Hence, the given condition of origin does not satisfy the given equation- $2x + y > 5$

Therefore, option A is not true for the given set of equations.
And it directly indicates that the open half-plane does not contain the origin.
Hence, the required answer is the solution set of the inequation $2x + y > 5$ is an Open half-plane not containing the origin.

Therefore option B is the correct answer.

Note: When the set of equations are given we can implement values and solve whereas, when we are given two sets of equations you can solve by any substitution or by elimination.