Solve the system of inequalities by graphing.
18x+6y ≥ 15
4x-8y > 32
To graph the system of inequalities, we will first graph the boundary lines for each inequality and then determine the shaded region that satisfies both inequalities.
1. Graph the line 18x+6y=15:
To graph the line, we can find two points and connect them.
When x=0, we have 6y=15 --> y=15/6 --> y= 2.5, so the first point is (0, 2.5).
When y=0, we have 18x=15 --> x=15/18 --> x= 0.83, so the second point is (0.83, 0).
Plotting these two points and connecting them, we get the line:
{{{ graph( 300, 200, -5, 5, -5, 5, -(3/9)x + 2.5) }}}
2. Graph the line 4x-8y=32:
Again, we find two points and connect them.
When x=0, we have -8y=32 --> y=-4, so the first point is (0, -4).
When y=0, we have 4x=32 --> x=8, so the second point is (8, 0).
Plotting these two points and connecting them, we get the line:
{{{ graph( 300, 200, -5, 5, -5, 5, (1/2)x-4) }}}
3. Now, we determine the shaded region that satisfies both inequalities. Since the first inequality is greater than or equal to, we shade the region above the line. Since the second inequality is greater than, we shade the region below the line.
The shaded region that satisfies both inequalities is the area bounded by the two lines and their respective shaded regions:
{{{ graph( 300, 200, -5, 5, -5, 5, -(3/9)x + 2.5, (1/2)x-4) }}}