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Which system of inequalities does the graph represent? Which test point satisfies both of the inequalities in that system?

The graph represents the system of inequalities 1. 4x - y is less than or equal to 4 and 2x - 2y is less than or equal to 3, 2. 4x - y is greater than or equal to 4 and 2x - 2y is less than or equal to 3, 3. 4x - y is less than or equal to 4 and 2x - 2y is greater than or equal to 3, 4. 4x - y is greater than or equal to 4 and 2x - 2y is greater than or equal to 3.

The test point satisfies both of the inequalities in the system represented by the graph.

Option 1: 4x - y is less than or equal to 4 and 2x - 2y is lesser than or equal to 3

Step-by-step explanation:

Equation of the red line:

m = (0-(-1.5))/(1.5-0) = 1

c = -1.5 (y intercept)

y = x - 1.5

The region lies above this line, so

y > x - 3/2

2y > 2x - 3

3 > 2x - 2y

2x - 2y < 3

Equation of the blue line:

m = (0-(-4))/(1-0) = 4

c = -4 (y intercept)

y = 4x - 4

Region lies above this line. So

y > 4x - 4

4 > 4x - y

4x - y < 4

Test point (0,0)

2x - 2y < 3

2(0) - 2(0) < 3

0 < 3 (true)

4x - y < 4

4(0) - 0 < 4

0 < 4 (true)

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.