Answer:
2x + y ≥ 4, y < x + 1
Explanation:
the thick (means we use ≤ or ≥) blue line that goes from top left to bottom right has a negative gradient, and it passes through (0,4).
taking the axes ((0,4) and (2,0)) intercepts into account, the gradient =
(4-0)/(0-2) = 4/-2 = -2.
the equation of the line is y - 0 = -2 (x - 2) = -2x + 4
that is y = -2x + 4. purple is shaded to the right of it. so we need y ≥ -2x +4,
y + 2x ≥ 4.
the dotted (meaning we use < or >) red line has a positive gradient. this line goes from bottom left corner of one square to top right of same square. it does this for all squares it passes through. we can see that the gradient is 1.
it passes through point (0 , 1).
equation of line = y - 1 = 1(x - 0) = x
y = x + 1.
purple is shaded below it. so we have y < x + 1.