which system of inequalities is represented by the graph?

a) y ≤ x - 5 and y ≥ -3x + 2

b) y ≤ x - 5 and y ≥ -3x - 2

c) y ≤ -x + 5 and y ≥ 3x - 2

d) y ≤ x + 5 and y ≥ -3x - 2

Option B) y ≤ x - 5 and y ≥ -3x - 2

Step-by-step explanation:

step 1

Find the equation of the inequality with y-intercept -5

The equation of the solid line has a positive slope

Take the ordered pairs (0,-5) and (4,-1) to find the slope

The equation of the solid line is

The solution of the inequality is the shaded area below the solid line

therefore

The equation of the first inequality is

step 2

Find the equation of the inequality with y-intercept -2

The equation of the solid line has a negative slope

Take the ordered pairs (0,-2) and (1,-5) to find the slope

The equation of the solid line is

The solution of the inequality is the shaded area above (to the right) the solid line

therefore

The equation of the second inequality is

step 3

The system of inequalities is

Option B is the correct one.

Step-by-step explanation:

The first graph passes through the points (0,-2).

Hence, the inequality equation maybe y ≥ - 3x - 2 or y ≥ 3x - 2.

Therefore, options B, C, D can be correct.

Again, the other graph passes through the point (0,-5).

Hence, the inequality equation that can be the solution is y ≤ x - 5.

Therefore, inequality A or B can be the answer.

Hence, combining those two conditions option B is the correct one. (Answer)

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