Mathematics Class 10
Pair of Linear Equations in Two Variables
Solve pairs of equations, predict the verdict from six numbers, and check the answer against the story.
13 lessons · ~100 min total
Track progress — 0 of 13 lessons read 0%
Lessons in this topic
- 0 Start here What this chapter is about, in one picture. · 5 min You are here
- 1 The pair, the picture, the verdict A linear equation in two letters draws a line; a pair of them crosses once, runs parallel, or lands on one line — exactly one solution, none, or infinitely many. · 8 min
- 2 A story becomes a pair Two conditions in a story give two equations: name the letters first, write one claim per condition, then solve. · 8 min
- 3 Three ratios, one verdict Write each equation as a₁x + b₁y + c₁ = 0 and compare the three ratios — unequal first ratios mean one pair, equal first two with a different third mean none, all three equal mean infinitely many. · 9 min
- 4 Predict, then look The ratio test predicts the verdict; a small sketch can still look parallel when the true crossing sits just outside it, so predict first and let the algebra settle it. · 8 min
- 5 Same line, new clothes Clear fractions and brackets first, then compare. Multiplying a whole equation by a number that is not 0 keeps the line. · 8 min
- 6 Two methods, one point A bare letter invites substitution; matching or scaled coefficients invite elimination — pick the cheap method, and let both methods land on the same pair. · 9 min
- 7 No answer, or every answer No common point means the facts clash. A whole shared line means one fact said twice. The ratios tell you which. · 9 min
- 8 Read the answer back A solved pair is not yet an answer: check it in both original equations, answer the question asked, then ask whether the world can carry it. · 8 min
- 9 Draw the pair, read the crossing Find two points on each line, join them, and read the crossing. Then check it in both equations. · 8 min
- 10 Checkpoint: clothes, methods, endings and graphs Five quick checks on the later ideas, from new clothes to graphs. · 6 min
- 11 The big picture The whole chapter on one screen. · 6 min
- 12 Track quiz Cheat-sheet table plus a reveal quiz — one question per idea. · 8 min
0%
Take this year's practice exam →
Draws questions from every track in this subject's year, not just this one — a Practice result, never official.