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MathidiaMathematics Academy
Simultaneous equations
Lesson 28 of 75
Standard practice

Elimination by subtraction

Objective. Eliminate one unknown by subtracting equations.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Elimination by subtraction develops a connected mathematical idea rather than an isolated trick. Find values satisfying two linear relationships at once. Begin by representing the quantities or relationships, choose a rule that fits, justify each transformation, and finish by checking units, signs, scale and whether the answer is reasonable.

Worked example

Select the intersection of y = x and y = 4 − x.

4
Coordinate grid with the line 4
  1. 1Identify the known information, the unknown and any conditions.
  2. 2Choose a diagram, table, graph or algebraic representation that exposes the structure.
  3. 3Apply the relevant rule one justified step at a time, keeping exact values where useful.
  4. 4Check by substitution, inverse reasoning or estimation. The result is (2, 2).

Answer: (2, 2)

Concept mastery

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Practice

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Common mistake. A common error in elimination by subtraction is to copy a procedure without checking its conditions. Label the structure first and justify every sign, operation and unit.

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