Question

Which graph represents the system 3x + 5y ≤ 9 and 2x + y ≥ 5?

Answer 1

Graph 1 represents the system.

Explanation:

The system of equations is given by,

`3x + 5y\leq 9`

`2x + y\geq 5`

Now, 'Zero Test' states that,

'If after substituting (0,0) in the inequalities the result is true, then the solution region is towards the origin. If the result is false, then the solution region is away from the origin'.

So, substituting (0,0), we get,

`3x + 5y\leq 9` implies 0≤9, which is true.

Then, the solution region is towards the origin.

`2x + y\geq 5` implies 0≥5, which is false.

Then, the solution region is away from the origin.

Hence, graph 1 represents the system.