PLEASE HELP ME!Which graph represents the solution set of the system of inequalities?−2x+y≤4y≥x+2

Accepted Solution

Answer:Bottom left graphStep-by-step explanation:We have to use what is called the zero-interval test [test point] in order to figure out which portion of the graph these inequalities share:−2x + y ≤ 4 >> Original Standard Equation+ 2x + 2x_________y ≤ 2x + 4 >> Slope-Intercept Equation−2[0] + 0 ≤ 40 ≤ 4 ☑ [We shade the part of the graph that CONTAINS THE ORIGIN, which is the right side.][tex]\displaystyle y > x + 2 \\ \\ 0 ≯ 2[/tex][We shade the part of the graph that does not contain the origin, which is the left side.]So, now that we got that all cleared up, we can tell that the graphs share a region in between each other and that they both have POSITIVE RATE OF CHANGES [SLOPES], therefore the bottom left graph matches what we want.** By the way, you meant [tex]\displaystyle y > x + 2[/tex]because this inequality in each graph is a dashed line. It is ALWAYS significant that you be very cautious about which inequalities to choose when graphing. Inequalities can really trip some people up, so once again, please be very careful.I am joyous to assist you anytime.