A party rental company has chairs and tables for rent. The total cost to rent 9 chairs and 7 tables is $\$ 86$. The total cost to rent 3 chairs and 5 tables is $\$ 52$. What is the cost to rent each chair and each table? Cost to rent each table: $s$

Step 1 ：We have a system of linear equations: \(9c + 7s = 86\) and \(3c + 5s = 52\)

Step 2 ：Multiply the second equation by 3: \(9c + 15s = 156\)

Step 3 ：Subtract the first equation from the second: \(8s = 70\)

Step 4 ：Solve for s: \(s = \frac{70}{8} = 8.75\)

Step 5 ：Substitute s back into the first equation: \(9c + 7(8.75) = 86\)

Step 6 ：Solve for c: \(c = \frac{86 - 7(8.75)}{9} = 2.75\)

Step 7 ：\boxed{\text{Final Answer: The cost to rent each chair is $2.75, and the cost to rent each table is $8.75.}}