Question

Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.y < 1/3x - 2y ≤ -1/6x - 5

Answer 1

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:

`\begin{gathered} 0\text{ =}(1)/(3)x-2 \\ 2=(1)/(3)x \\ 2\cdot3=x \\ 6\text{ = x} \end{gathered}`

(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:

`\begin{gathered} 0\text{ =- }(1)/(6)x-5 \\ 5=-(1)/(6)x \\ 5\cdot(-6)\text{ = x} \\ -30\text{ = x} \end{gathered}`

(-30 , 0)

graph solution:

The answer is:

The solution to the system: Unbounded