Question

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

Answer 1

Answer: Region Q

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Step-by-step 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).

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

`5x + 15y \ge -20\\\\5(0) + 15(0) \ge -20\\\\0 \ge -20\\\\`

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.

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To summarize so far, we found that

• regions Q and R make 4x-2y > 6 true,
• regions P and Q make
  `5x + 15y \ge -20\\\\` true.

The overlap is region Q which is the final answer

Any point from region Q satisfies both 4x-2y > 6 and
`5x + 15y \ge -20\\\\` 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.

Answer 2

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