Which section of the graph represents the solution of the system of inequalities shown?

Q

Step-by-step explanation:

5x+15y ≥ -20

Solve for y

15 y≥  -5x-20

Divide by 15

y ≥ -5x/15 -20/15

y ≥ -1/3 x -4/3

Y is greater than or equal to so shade above  and on the line

4x-2y > 6

Solve for y

-2y > -4x+6

y < 2x -3

Shade below the line

The double shaded area is the solution

==========================================================

Explanation:

Let's focus on the inequality 4x-2y > 6

Plug in (x,y) = (0,0) to find that...

4x-2y > 6

4(0)-2(0) > 6

0 > 6

This is a false statement. So that means (0,0) is not in the shaded region for 4x-2y > 6. So we'll shade the opposite side of the dashed line to shade regions Q and R (i.e. stuff below the dashed line).

-----------------

Let's check the point (0,0) with the other inequality as well

This is true because 0 is to the right of -20 on the number line.

So we'll shade regions P and Q to represent the solution set for this inequality. These regions are above the boundary line. Points on the boundary are also included.

------------------

To summarize so far, we found that

The overlap is region Q which is the final answer

Any point from region Q satisfies both 4x-2y > 6 and at the same time. A point on the solid boundary line is part of the solution set, but stuff on the dashed boundary line are not solution points.

hi how are you doing today? if you ever need just tell me

step-by-step explanation: