Question

I need help on problem 12 and only problem 12 please

Answer 1

12.

In order to solve this system of inequalities, let's graph each inequality in the coordinate plane and then find the solution region.

To graph an inequality, first let's graph the corresponding equation, then we use the inequality symbol to determine the solution region.

Graphing the equation 3x + 3y = 1, let's determine two ordered pairs that are solution to this equation. Using x = 0 and x = 1, we have:

`\begin{gathered} x=0\colon \\ 0+3y=1\to y=(1)/(3) \\ x=1\colon \\ 3+3y=1\to y=-(2)/(3) \end{gathered}`

Now, for 2y = 11, we have the horizontal line y = 11/2.

For both inequalities, the line is not part of the solution, because the symbols are "greater than" and "lesser than", so we draw the line dashed.

Graphing both inequalities in green and blue, and the solution region in yellow, we have: