In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
y < 1/3x - 2
y ≤ -1/6x - 5
Step 02:
system of inequalities:
ineq. 1:
y < 1/3x - 2
graph the line 1:
y = 1/3x - 2
if x = 0:
y = 1/3(0) - 2 = 0 - 2 = - 2
(0, -2)
if y = 0:
[tex]\begin{gathered} 0\text{ =}\frac{1}{3}x-2 \\ 2=\frac{1}{3}x \\ 2\cdot3=x \\ 6\text{ = x} \end{gathered}[/tex](6, 0)
ineq. 2:
y ≤ -1/6x - 5
graph the line 2:
y = -1/6x - 5
if x = 0:
y = -1/6(0) - 5 = 0 - 5 = - 5
(0 , -5)
if y = 0:
[tex]\begin{gathered} 0\text{ =- }\frac{1}{6}x-5 \\ 5=-\frac{1}{6}x \\ 5\cdot(-6)\text{ = x} \\ -30\text{ = x} \end{gathered}[/tex](-30 , 0)
graph solution:
The answer is:
The solution to the system: Unbounded
