Which graph represents the solution set for the system x + y ≥ 5 and -3x + 2y ≤ -2.

B

Step-by-step explanation:

I like to put inequalities in the form y ≤ or ≥ mx + b. It makes it easier to tell which line is which on the graph. So x + y ≥ 5 can be put as y ≥ -x + 5. Next, -3x + 2y ≤ -2 can be put as 2y ≤ 3x -2. This should be further simplified by dividing everything by 2, isolating y, to y ≤ x - 1. Now since b is the y-intercept, we know that the first inequality (x + y ≥ 5 or y ≥ -x + 5) is represented by the blue line. Since in the new form we put that inequality in (y ≥ -x + 5), the shaded part must be above the line. This means that graph A is not the answer. Next, we know that the second inequality is represented by the red line. We also know that the shaded part must be below the line, which means that it cannot be graph C. It is cannot be graph D because the shaded parts must satisfy BOTH (hence, AND. If it said OR it would be different) inequalities. This leaves B as the only correct answer.