Recomposition Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
You find x=3x=3 and y=1y=1 from solving a system. Recompose by substituting back into both equations to verify.

Solution

  1. 1
    Equation 1: 2(3)+1=72(3)+1 = 7. True.
  2. 2
    Equation 2: 3−1=23-1 = 2. True.
  3. 3
    Both equations are satisfied — the solution (3,1)(3,1) is verified.

Answer

(x,y)=(3,1)  ✓(x,y)=(3,1)\;\checkmark
Recomposition (verification by back-substitution) confirms that the decomposed solution actually satisfies the original problem. It is an essential error-checking step.

About Recomposition

Recomposition is the process of combining simpler parts, sub-results, or solved sub-problems back together to form a complete solution or to understand the whole structure from its pieces.

Learn more about Recomposition →

More Recomposition Examples

Example 1 easy

After decomposing [formula], recompose to solve [formula].

Example 2 medium

Partial fractions gave [formula]. Recompose to verify by adding the fractions.

Example 4 medium

Given the identity [formula], recompose: use it to evaluate [formula].

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Related Concepts

Decomposition