The phrase " no more than " means in inequality
[tex]\leq[/tex]
The phrase " at least" means in inequality
[tex]\ge[/tex]
Since she earns $6 per hour for each job, then
Let the number of hours for the first job is x and the number of the hours for the second job is y,
Since she needs to earn at least $60, then the first inequality should be
[tex]6x+6y\ge60[/tex]
Divide each term by 6
[tex]\begin{gathered} \frac{6x}{6}+\frac{6y}{6}\ge\frac{60}{6} \\ \\ x+y\ge10 \end{gathered}[/tex]
Subtract x from both sides
[tex]\begin{gathered} x-x+y\ge-x+10 \\ y\ge-x+10\rightarrow(1) \end{gathered}[/tex]
Since she wants to work no more than 12 hours, then the second inequality should be
[tex]x+y\leq12[/tex]
Subtract x from both sides
[tex]\begin{gathered} x-x+y\leq-x+12 \\ y\leq-x+12\rightarrow(2) \end{gathered}[/tex]
The correct system is
[tex]\begin{gathered} y\leq-x+12 \\ y\ge-x+10 \end{gathered}[/tex]
The answer is A
