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Inequalities are used to represent unequal expressions
The system of inequalities is: [tex]y > x + 1[/tex] and [tex]y \ge -x + 4[/tex]
The first line passes through the following points:
(-1, 0) and (0,1)
So, we start by calculating the slope (m)
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
This gives
[tex]m = \frac{1 -0}{0--1}[/tex]
[tex]m = \frac{1}{1}[/tex]
[tex]m = 1[/tex]
The equation is then calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
So, we have:
[tex]y = 1(x -0) + 1[/tex]
[tex]y = x + 1[/tex]
The line is a dotted line, and the upper part is shaded.
So, the inequality is:
[tex]y > x + 1[/tex]
Using the same steps above, the equation of the second line is:
[tex]y = -x + 4[/tex]
However, the line is a closed line, and the upper part is shaded.
So, the inequality is::
[tex]y \ge -x + 4[/tex]
Hence, the system of inequalities are:
[tex]y > x + 1[/tex] and [tex]y \ge -x + 4[/tex]
Read more about systems of inequalities at:
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