Graph each inequality separately. The overlapping region will be the solution of the system.
Practice makes perfect
To solve the given system by graphing, we should first draw each inequality separately. Then we will combine the graphs. The overlapping region will be the solution set. Let's start!
Inequality I
To determine the boundary line of the first inequality, we need to exchange the inequality symbol for an equals sign.
Inequality:& |y|>2
Boundary Line:& |y| =2
Since the boundary line is an absolute value equation we need to consider two cases.
|y|=2 ⇒ lc y ≥ 0:y = 2 & (I) y < 0:y = - (2) & (II)
We got two equations and both of them will be the boundary lines of the given inequality. Notice that they will be dashed because the inequality is strict.
Next, we need to decide if we should shade the space between those lines or not. We can do this by testing a point that does not lie on the boundary line. If the point satisfies the inequality, it lies in the solution set. If not, we will shade the other regions. Let's use (0,0).
Because (0,0) created a false statement, we will shade the regions that do not contain this point.
Inequality II
Now that we've completed the first inequality, let's determine the boundary line of the second inequality. We will follow the same process once more.
Inequality:& x>3
Boundary Line:& x=3
This boundary line is a vertical line. The inequality x>3 describes all values of x that are greater than 3. This means that every coordinate pair with an x-value that is greater than 3 needs to be included in the shaded region. Notice that the inequality is strict, so the boundary line also will be dashed.
Combining the Inequality Graphs
In drawing the inequality graphs on the same coordinate plane, we are able to see the overlapping section. This is the solution set of the system.
Finally, we can view only the solution set by removing the shaded regions that are not overlapping.
