Determine the inequality symbol and complete the inequality
In this exercise, we have been given the graph of a system of two linear inequalities. We will tackle them one at a time and bring them together in a system at the end.
The Red Inequality
Let's take a look at the graph of the red inequality.
We can see that the boundary line is horizontal and passes through (0, 3). Therefore, the equation of the line is y= 3. To finish forming the inequality, we need to determine the inequality symbol. This means substituting the equals sign with a blank space, since it is still unknown to us.
y ? 3
To figure out what the symbol should be, let's substitute any point that lies within the solution set into the equation.
We will substitute ( 0, 0) for this test, and then make the inequality symbol fit the resulting statement.
0 is less than 3, so the symbol will be either < or ≤. Since the boundary line in the given graph is solid, the inequality is not strict, and we can form the first inequality in the system.
y ≤ 3
The Blue Inequality
Writing the inequality for this region of the graph will involve the same steps as above.
Notice that the boundary line is vertical and passes through ( 2,0). Therefore, the equation of the line is x= 2. Once more, we substitute the equals sign with a blank space.
x ? 2
We will need another point that lies within the solution set to determine the sign of this inequality.
We will substitute ( 0, 0) for this test, and then make the inequality symbol fit the resulting statement.
0 is less than 2, so the symbol will be either < or ≤. Since the boundary line in the given graph is solid, the inequality is not strict, and we can form the second inequality in the system.
x≤ 2
Writing the System
To complete the system of inequalities, we will bring both of our inequalities together in system notation.
y≤ 3 x≤ 2
