The Math Meridian
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Systems of equations in three unknowns

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Useful for: IB Math AA HL

Learn it Use elimination to remove one variable from two pairs of equations, leaving a 2 × 2 system. Solve it, then substitute back for the third variable.

Example: x + y + z = 6, x − y + z = 2, 2x + y − z = 1.

  1. Add eq 1 and 2: 2x + 2z = 8. Add eq 1 and 3: 3x + 2y = 7 … giving x = 1, y = 2, z = 3.

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