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Linear Equations in Two Variables

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Take 2x + 3y = 12. Here x and y are two rupee amounts. What are they?

Two claims. One shared point?

This chapter is Linear Equations in Two Variables. One equation has many answers. Two equations can have exactly one.

What you will learn

  • Two letters. One equation, two unknowns. A solution is a pair.
  • Checking a pair. Put the pair in. Both equations must be true.
  • One line, many pairs. Every solution sits on one line.
  • Where two lines meet. The point that answers both equations.
  • When lines refuse. Three things two lines can do.
  • Substitution. Name one letter, then use its name.
  • Scale, then subtract. Match one letter's coefficients, then subtract.
  • Both roads agree. Two methods, one true answer.
  • What the algebra says. What is left decides how many solutions.

Need a quick catch-up?

These earlier ideas help. Revisit any one that feels unsure.

  • One point needs two numbers. Order matters.
  • Reading a line: steepness is a change per step.
  • The number in front of a letter is its coefficient.
  • The balance: both sides of an equation name one number.
  • Moving a term across the equals sign.
  • Putting an answer back in to check it.

Jump to lesson

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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