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Year 9 · Patterns & Algebra

Simultaneous equations

Simultaneous equations are two equations with two unknowns, true at the same time.

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How to do it

  1. Make the coefficient of one letter the same in both equations.
  2. Add or subtract the equations to remove that letter.
  3. Solve for the other letter, then substitute back.

Worked example

Solve the simultaneous equations 3x + y = 21 and 3x − 3y = 9. What is x?
Use elimination: multiply the equations so one variable has matching coefficients, then add or subtract to remove it. Solving gives x = 6 and y = 3. Check in the first equation: 3×6 + 1×3 = 21 ✓
Answer: 6

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Check both answers in both equations.

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