Canister inventory and graphical solution

A laboratory storeroom contains \(44\) canisters with a total capacity of \(172\) litres. Small canisters hold \(3\) litres and large canisters hold \(5\) litres. Let \(s\) be the number of small canisters and \(l\) be the number of large canisters.

1. Form two equations in \(s\) and \(l\).
2. Copy and complete the following tables of values of \(s\) and \(l\) for the equations \(s+l=44\) and \(3s+5l=172\).
   For the equation \(s+l=44\):

   \(s\)	\(0\)	\(22\)	\(44\)
   \(l\)

   For the equation \(3s+5l=172\):

   \(s\)	\(4\)	\(24\)	\(44\)
   \(l\)

3. On the grid provided below, using a scale of 1 cm to represent 5 units on both axes, draw and label the graphs of \(s+l=44\) and \(3s+5l=172\) for \(0\leq s\leq50\) and \(0\leq l\leq50\).
4. Hence, use the graphs to find the numbers of small and large canisters.