Graph the solution set of the system of inequalities or indicate that the system has no solution

Question

Graph the solution set of the system of inequalities or indicate that the system has no solution

2x+y<8

Answer 1

2x + y < 8

you can solve this for x or for y

y< 8-2x

x < (8-y)/2 = 4 - y/2

graph the inequality by graphing 2x+y =8 as a dotted line to indicate the inequality graph does not include the line, but that the line is on the edge of the solution set, its boundary

2x+y= 8 is most easily graphed by plotting the x and y intercepts and connecting the with a straight line through them y intercept is 8 or the point (0,8) x intercept is 4 or the point (4,0)

then shade one side of the dotted line. check the origin (0,0) it satisfies the inequality as 0 +0 = 0 which is less than 8. so shade all the area below and to the left of the dotted line