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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

B) y ≤ x - 5 and y ≥ -3x - 2

Step-by-step explanation:

Look at the graph. An easy way to solve this question is to first figure out where the y-intercepts of each axis are. I see one at -5 and another at -2. Therefore, we can eliminate any answers that have "b" in the "y = mx +b" equation equal to anything that is not -5 or -2. Those two options would be A and D. With A and D gone, we have B and C left.

What do we do now? We look at the slope of each line. We can see that from left to right, one is going up and the other is going down. Therefore, one is positive and one is negative, so in the y = mx + b equation, one "m" should be positive and the other negative. We see that option B displays this, so that's our answer.

You can also double-check this on any graphing website to see if the equation given in B matches the graph you were given.

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step-by-step explanation: