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_____________________________________ .The test point_______ satisfies both of the inequalities in the system represented by the graph.

Answer:1) The inequality for the given system are y ≥ 4x - 4y ≥ x - 1.52)  The test point (0,0)  satisfies both of the inequalities in the system represented by the graph.Step-by-step explanation: Given : A graph showing  a system of inequalities.We have to find the system of inequality. For line 1) The points that cut the x and y axis are (1,0) and (0,-4)Thus, we can find the equation of line using two given point.Since the general equation of line is y = mx + c Where m is slope and c is y interceptSlope is find as [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Substitute, we get,[tex]m=\frac{-4-0}{0-1}=4[/tex]Slope is 4.Thus, equation becomes y = 4x + cFor c put (0,-4)  in the above equation , we have,-4 = 4(0) + c ⇒ c = -4 Thus, equation becomes y = 4x - 4For inequality take a test point (0,0) and we check for which inequality it satisfies the graph regionFor (0,0) y = 4x - 4 becomes 0 = - 4  is satisfied when 0 > -4 thus, the inequality becomes y ≥ 4x - 4Since, the line is a solid so it will take up equality sign too.For line 2) The points that cut the x and y axis are (1.5,0) and (0,-1.5)Thus, we can find the equation of line using two given point.Since the general equation of line is y = mx + c Where m is slope and c is y interceptSlope is find as [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Substitute, we get,[tex]m=\frac{-1.5-0}{0-1.5}=1[/tex]Slope is 1.Thus, equation becomes y = x + cFor c put (0,-1.5)  in the above equation , we have,-1.5 = (0) + c ⇒ c = - 1.5 Thus, equation becomes y = x - 1.5For inequality take a test point (0,0) and we check for which inequality it satisfies the graph regionFor (0,0) y = x - 1.5 becomes 0 = -1.5  is satisfied when 0 > - 1.5 thus, the inequality becomes y ≥ x - 1.5Since, the line is a solid so it will take up equality sign too. Thus, the inequality for the given system are y ≥ 4x - 4y ≥ x - 1.5Also,  The test point (0,0)  satisfies both of the inequalities in the system represented by the graph.