There are many systems of equation that will satisfy the requirement for Part A. an example is y≤(1/4)x-3 and y≥(-1/2)x-6 y≥(-1/2)x-6 goes through the point (0,-6) and (-2, -5), the shaded area is above the line. all the points fall in the shaded area, but y≤(1/4)x-3 goes through the points (0,-3) and (4,-2), the shaded area is below the line, only A and E are in the shaded area. only A and E satisfy both inequality, in the overlapping shaded area.
Part B. to verify, put the coordinates of A (-3,-4) and E(5,-4) in both inequalities to see if they will make the inequalities true. for y≤(1/4)x-3: -4≤(1/4)(-3)-3 -4≤-3&3/4 This is valid. For y≥(-1/2)x-6: -4≥(-1/2)(-3)-6 -4≥-4&1/3 this is valid as well. So Yes, A satisfies both inequalities. Do the same for point E (5,-4)
Part C: the line y<-2x+4 is a dotted line going through (0,4) and (-2,0) the shaded area is below the line farms A, B, and D are in this shaded area.
