Solving a word problem using a system of linear equations of the form Ax + By = C

Question

A party rental company has chairs and tables for rent. The total cost to rent 8 chairs and 4 tables is $45. The total cost to rent 3 chairs and 2 tables is $21. What is the cost to rent each chair and each table?

Answer 1

8c + 4T = 45

3C +2T = 21

multiply the 2nd equation by 2 and subtract from the 1st equation to eliminate one variable

6C+4T = 42

8C -6C = 45-42

2C = 3

C = $1.50 per chair

2T = 21-3C = 21-4.5 = 16.5

T = 16.5/2 = $8.25 per table