7.1Systems of Linear Equations: Two Variables
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Study this section
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What leans on this
Chemistry that uses this algebra — the answer to why you are learning it.
The book balances entirely by inspection and never sets up equations, but every balance-by-inspection problem with two adjustable coefficients (fix one at 1, solve for the other from one atom-balance constraint) is quietly a 2×2 linear system — a much more concrete first encounter with 'why would I want two equations in two unknowns' than an abstract mixture problem.
- Alongside9.3Enthalpy
Hess's law is linear combination of equations: scale a reaction (and its ΔH) by a constant, reverse another (negating its ΔH), then add so intermediates cancel — exactly the multiply-then-add elimination method for two-variable systems, just eliminating a chemical species instead of x.
- Applies12.4Free Energy
Coupled reactions reuse the Hess's-law addition trick from chapter 9 on ΔG instead of ΔH — decomposing ZnS (ΔG°=+201.3 kJ) is made spontaneous by adding the oxidation of sulfur (ΔG°=−300.1 kJ) so the shared S(s) cancels, the identical scale-and-add-to-eliminate-a-species move as solving a linear system by elimination.