Question

If you graph the system of inequalities given below, which points would lie in the solution set. Select all the correct answers

Answer 1

Answer choices: (-2,3) (-1,3) (0,0) (2,-2) (3,5)
And the inequalities are x-y≥-4, 2x-y≤5, 2y+x>1

graph the lines
x-y=-4
2x-y=5
2y+x=1
test if (0,0) is in the zone with original inequality
if it isn't, shade to other side
if it is, shad including (0,0)

if you have < or >, use dotted line
if you have ≤ or ≥, use solid line
first one, (0,0) is not, so shade where (0,0) Isn't
2nd equation, (0,0) is in, so shade wher (0,0) is
3rd equation, (0,0) is not, so shade wher (0,0) isnt

resulting graph included below
the triangle where all 3 graphs intersect is solution
as you can see, the solutins are (-1,3) and (3,5)
(-1,3) is a solution because it is on the line and the line is solid so it includes those values on the line