Solving systems by elimination

Solving systems by elimination

Solving systems by elimination

Elimination works best when both equations are in the form ax + by = c. The idea is to make one variable cancel when you add or subtract the equations.

A worked example

2x + y = 7

x − y = −1

Add the two equations: the +y and −y cancel, leaving 3x = 6, so x = 2. Put x = 2 into the second equation: 2 − y = −1 → y = 3. The solution is (2, 3).

When nothing cancels yet

If neither variable cancels straight away, multiply one or both equations by a number so a pair of coefficients match in size. Then add (if the signs are opposite) or subtract (if they are the same).

Three rules that always help

  • Use elimination when both equations are in standard form.
  • Make a pair of coefficients equal in size, then add or subtract to cancel.
  • Solve for the remaining variable, substitute back, and check.

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