MEPX
Chapter 7 of 10All chapters
  1. 1Why letters
  2. 2Rearranging
  3. 3Expanding and factorising
  4. 4Straight lines
  5. 5Quadratics
  6. 6Fractions and powers
  7. 7Two unknowns
  8. 8Inequalities
  9. 9Functions
  10. 10Turning words into algebra

Chapter 7 of 10

Two unknowns

Simultaneous equations.

Two methods

Substitution rearranges one equation and puts it into the other. Elimination adds or subtracts the equations to cancel a variable. Both reduce two unknowns to one.

  • Two unknowns need two independent equations.
  • Graphically, the solution is where the two lines cross.

No solution

Parallel lines never meet, so the equations contradict. Identical lines meet everywhere, so there are infinitely many solutions.