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:& 8x+4y< 10
Boundary Line:& 8x+4y=10
Let's rewrite this equation in slope-intercept form.
y= - 2x+ 2.5
Using this information, we will plot the boundary line. Notice that the inequality is strict, so the boundary line will be dashed.
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) created a true statement, we will shade the region containing 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>|2x-1|
Boundary Line:& y=|2x-1|
The graph of this boundary line is the graph of the parent function y=|x| after transformations. Before we can identify them we will rewrite our equation.
y=|2x-1| ⇔ y= 2| x- 1/2|
Now we can identify a horizontal translation 12 units right and a vertical stretch by a factor of 2. The boundary line will be dashed because the inequality is strict.
