Question

Which graph represents the solution set for the system 2x + 5y ≤ 9 and 3x + 5y ≤ 9?

Answer 1

The graph representing the solution is given below.

Explanation:

We are given the system of inequality is,

`2x + 5y\leq  9`

`3x + 5y \leq  9`

Zero Test states that,

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

So, upon substituting (0,0) in the given inequalities, we get,

`2x + 5y\leq  9` implies 0≤ 9, which is true.

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

Thus, the solution region for both the inequalities is towards the origin.

Hence, upon plotting, the graph representing the solution set is given below.