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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.

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amna04352 amna04352 · Answer 1 · 2020-02-24T11:05:29+01:00

Answer:

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)