The big picture
One test, two methods, three checks. Then you write the answer.
| Idea | Remember | Example |
|---|---|---|
| The three verdicts | Cross once, run parallel, or lie on one line. | (7, 5); none; every point |
| A story becomes a pair | Name the letters. Write one equation for each fact. | samosa ₹10, chai ₹15 |
| Three ratios | a₁/a₂, b₁/b₂, c₁/c₂ decide the verdict. | one, none, infinitely many |
| Zoom out | Ratios first, picture second, algebra decides. | crossing at (11, 2) |
| New clothes | Clear denominators, open brackets, gather. Multiply every term by the same non-zero number. The line does not change. | 2x − 3y + 6 = 0 |
| Two methods | A letter alone: substitution. Matching terms: elimination. | y = 15, then x = 10 |
| Two odd endings | A false sentence: facts clash. 0 = 0: one fact twice. | 0 = 30; 0 = 0 |
| Reading it back | Check both equations. Answer the question. Can the story allow it? | 7 matches; half a box is not allowed |
| Draw and read | Find two points on each line. Join them. Read where they cross. | 2x + y = 8 and x − y = 1 meet at (3, 2) |
Open Chapter 3 now. You know every idea in it. Try its exercises.