Pair of Linear Equations in Two Variables — Class 10 CBSE Mathematics revision notes
A 4-page visual revision sheet for Pair of Linear Equations in Two Variables, written for Class 10 CBSE Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
What this Pair of Linear Equations in Two Variables sheet covers
- Introduction
- The standard form of a pair
- first equation
- second equation
- neither may vanish completely
- a solution is a point of the plane
- Graphical Method of Solution
- Consistency and Number of Solutions
- Three things two lines can do
- Intersecting
- Parallel
- Coincident
- Reading the lines off the grid
- Drawing the two lines
- The ratio test, as one decision
- Testing a point against the pair
- does (2, 3) satisfy 2x+3y=13
- and the second line x-y=-1
- both hold, so the solution is
- while (5, 1) only manages the first
- One equation, and then two
- Algebraic Methods
- Substitution Method
- Elimination Method
- The ratio test on three real pairs
- 2x+3y-5=0 with 4x+6y-15=0
- 2x+3y-5=0 with 4x+6y-10=0
- 2x+3y-13=0 with x-y+1=0
- Which method to reach for
- Choosing k so the pair behaves
- for kx+2y-5=0 with 3x+y-1=0
- one solution needs the first two apart
- no solution needs them equal, c apart
- so k=6 is the single value that fails
- Cross Multiplication Method
- Cross multiplication
- with both in a x + b y + c = 0 form
- on 2x+3y-13=0 and x-y+1=0
- next term
- last term
- so the point is
- Equations reducible to a linear pair
- given
- swap in
- the pair turns linear
- solve, then undo the swap
- Symbols
- Turning words into a pair
- A two digit number, worked through
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Pair of Linear Equations in Two Variables the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.