Decomposition Math Example 3

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Example 3

easy
Decompose solving the system 2x+y=72x + y = 7 and x−y=2x - y = 2 into steps.

Solution

  1. 1
    Step 1 — Eliminate yy: add the two equations: 3x=93x = 9, so x=3x = 3.
  2. 2
    Step 2 — Back-substitute: 3−y=23 - y = 2, so y=1y = 1.

Answer

x=3,y=1x=3,\quad y=1
Solving a system is decomposed into: elimination to reduce to one variable, then back-substitution. Each sub-problem is simpler than the original.

About Decomposition

The strategy of breaking a complex mathematical object or problem into simpler, independent subproblems that can be solved separately.

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More Decomposition Examples

Example 1 easy

Factorise [formula] by decomposing the expression into simpler parts.

Example 2 medium

Decompose the partial fraction [formula] into the form [formula].

Example 4 medium

Decompose the proof that [formula] is irrational into logical sub-goals.

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Related Concepts

Recomposition