The system of linear inequalities that are graphed are {y≥3x−2 and x+2y≤4
In order to get the required system of inequalities, we need to get the equations of both lines.
For the line with having the coordinate points (0, 2) and (4, 0)
The standard form of the expression will be y = mx+b
m = 0-2/4-0
m = -2/4
m = -1/2
The y-intercept "b" is 2 (the point where the line cuts the y-axis)
The equation of the line will be y = -1/2x + 2
2y = -x + 4
x + 2y = 4
Since the line is a solid line and shaded towards the negative side of the graph, the given inequality expression will be x+2y ≤ 4
For the line with having the coordinate points (0, -2) and (2, 4)
The standard form of the expression will be y = mx+b
m = 4+2/2-0
m = 6/2
m = 3
The y-intercept "b" is -2 (the point where the line cuts the y-axis)
The equation of the line will be y = 3x-2
Since the line is a solid line and shaded towards the positive side of the graph, the given inequality expression will be y≥3x−2
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