Let x be the number of hours Gavin works as lifeguarding and y be the number of hours he works walking dogs, then we can set the following system of inequalities:
[tex]\begin{gathered} x+y\le10, \\ 20x+6y\ge90. \end{gathered}[/tex]
Solving the first inequality for y, we get:
[tex]\begin{gathered} x+y\le10, \\ y\le10-x\text{.} \end{gathered}[/tex]
Solving the second inequality for y we get:
[tex]\begin{gathered} 20x+6y\ge90, \\ 6y\ge90-20x, \\ y\ge15-\frac{20}{6}x\text{.} \end{gathered}[/tex]
Answer: Inequality 1
[tex]y\le10-x\text{.}[/tex]
Inequality 2
[tex]y\ge15-\frac{20}{6}x_{}\text{.}[/tex]
Now, to find a solution we overlap the above graphs:
A possible solution is x=5 and y=4.
