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Graphing Systems of Inequalities
The graph of these two inequalities is shown below:
The shaded area includes all the solutions to this system of inequalities. The points along the line of y = 2x + 3 are included in the solutions. The points along the line y = x + 1 are NOT included in the solutions. All solutions must be below the line for y = - x +1 and below or along the line y = 2x + 3.
Remember:
The solutions for y = 2x + 3 lie along the graph of the line y = 2x + 3
The solutions for y < 2x + 3 lie 'below' (in the negative y-axis direction) the graph of the line y= 2x + 3.
The solutions for y > 2x + 3 lie 'above ( in the positive y-axis direction) the graph of the line y = 2x + 3.
The solutions for y ≤ 2x + 3 lie both along the line and below the line of the graph of the line y = 2x + 3 , since ≤ means 'less than and equal to'.
The solutions for y ≥ 2x + 3 lie both along the line and above the line of the graph of the line y = 2x + 3 , since ≥ means 'greater than and equal to'.
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