Two 3D-printing materials

Flexible filament costs \(a\) cents per metre and rigid filament costs \(b\) cents per metre. An order of \(12\) m of flexible filament and \(18\) m of rigid filament costs \(\$8.70\). Another order of \(20\) m of flexible filament and \(10\) m of rigid filament costs \(\$9.50\).

1. Form two equations in \(a\) and \(b\) to represent the two orders.[2]
2. Solve the equations obtained in (a) to find \(a\) and \(b\).[3]
3. Hence, find the combined cost of \(5\) m of each material.[2]