Lesson 12 of 14
The big picture
Show on a big screenTwo letters, one canteen bill, and nine ideas.
| Idea | Remember |
|---|---|
| Two letters | ax + by + c = 0. Both letters have power 1, never multiplied. A solution is a pair. |
| Pass twice | Put the pair in both equations. One equation holding is not enough. |
| One line | Every pair of one equation lies on one line, and every point of it. |
| Two lines | Each equation draws a line. The crossing is the solution. |
| Three verdicts | Cross once, run parallel, or lie on one line: one, none, or every point. |
| Substitution | Name a letter with no number in front. Use its name in the other equation. Then solve. |
| Scale, then subtract | Match one letter's coefficients. Then subtract, and that letter cancels. |
| Both roads | Substitution and elimination cannot land on two answers. |
| The leftover | A 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.