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Linear Equations in Two Variables

The big picture

Two letters, one canteen bill, and nine ideas.

Linear Equations in Two Variables: nine ideas on one screen
IdeaRemember
Two lettersax + by + c = 0. Both letters have power 1, never multiplied. A solution is a pair.
Pass twicePut the pair in both equations. One equation holding is not enough.
One lineEvery pair of one equation lies on one line, and every point of it.
Two linesEach equation draws a line. The crossing is the solution.
Three verdictsCross once, run parallel, or lie on one line: one, none, or every point.
SubstitutionName a letter with no number in front. Use its name in the other equation. Then solve.
Scale, then subtractMatch one letter's coefficients. Then subtract, and that letter cancels.
Both roadsSubstitution and elimination cannot land on two answers.
The leftoverA letter in it means one solution. 0 = −6 means none. 0 = 0 means one line twice.

This topic is Linear Equations in Two Variables.

One habit helps in the whole chapter. Check any pair in both equations, not just one. Next comes geometry, which starts with the agreements every proof needs.

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This track

  1. 0 Start here
  2. 1 One claim with two letters
  3. 2 Checking a pair twice
  4. 3 All the pairs make a line
  5. 4 Two lines and one shared spot
  6. 5 The three things two lines can do
  7. 6 Checkpoint: claims, pairs and lines
  8. 7 The substitution walk
  9. 8 Scale the equations, then take one away
  10. 9 Both roads, one answer
  11. 10 What falls out when nothing is left
  12. 11 Checkpoint: the two algebra roads
  13. 12 The big picture
  14. 13 Track quiz

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