Which system of inequalities has a lot of solution?

(a) 2x + 4y ≥ 3 ; 2x + 4y ≤ 3

Step-by-step explanation:

When inequalities are involved, the resulting solution is generally a region since for a value of x, we have y greater than or less than a particular value and vice versa.

When a system of equations with inequalities are solved, the intersection of all the equations in the system is the solution.

In the first option, we see that the both equations have 2x+4y=3 as common. So, it is the solution of the first system of inequalities.

Similarly, the solution of second system of inequalities is 2x+4y>3 and the third system is none since they don't intersect at all.

Here, 2x+4y > 3 denotes a region and 2x+4y=3 is the equation of a straight line.

Hence the first system has a solution that is a line.

(for question 7: Its the last one)

(for question 8: its the first one)