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:& 2x+3y≥ 6
Boundary Line:& 2x+3y=6
Let's rewrite this equation in slope-intercept form.
y= -2/3x+ 2
Using this information, we will plot the boundary line. Notice that the inequality is not strict, so the boundary line will be solid.
Next, we need decide which side of the boundary line we should shade. 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 region. Let's use ( 0, 0).
Because (0,0) did not create a true statement, we will shade the region opposite 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:& y≤ |x-6|
Boundary Line:& y=|x-6|
The graph of this boundary line is the graph of the parent function y=|x| after transformations.
y=|x- 6|
We can identify a horizontal translation 6 units to the right. The boundary line will be solid because the inequality is notstrict.
