Linear Equations in Two Variables — Class 9 Maharashtra SSC Mathematics revision notes
A 4-page visual revision sheet for Linear Equations in Two Variables, written for Class 9 Maharashtra SSC 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.
Page 1 as PDF
Linear Equations in Two Variables in one look
a first look at solving two equations together, and at the line a single equation draws
One equation, endlessly many answers
- an equation such as 2x + 3y = 12 has two unknowns and the first power only, which is what makes it linear
- a solution is an ordered pair (x, y) making the equation true, and one equation has infinitely many of them
- to find some, choose a value for x and solve for y, then repeat. Choosing x = 0 and y = 0 gives the two axis crossings quickly
- plotting those pairs on the plane gives points that all lie on one straight line
- so a single linear equation describes a whole line, and every point of that line is a solution
- two such equations taken together are called simultaneous, and solving them means finding the pair that satisfies both at once
The methods, and when each is easiest
- Elimination: make one variable have the same coefficient in both equations, then add or subtract to remove it. The default choice, and usually the quickest
- Substitution: make one variable the subject of one equation and put that expression into the other. Best when a coefficient is already 1 or -1
- Graphical: draw both lines and read off where they cross. Asked for by name, and it needs at least two points per line, three being safer
- Equating: make the same variable the subject of both equations, then set the two expressions equal. A tidy variant of substitution
Page 1 of 4. The full sheet, all 4 pages, opens free in the app.
What this Linear Equations in Two Variables sheet covers
- Linear equation in two variables
- Solution of an equation
- One equation, endlessly many answers
- Substitution method
- Elimination method
- Graphical method
- The methods, and when each is easiest
- Elimination
- Substitution
- Graphical
- Equating
- Elimination in full
- Adding or subtracting, decided properly
- Drawing the graph properly
- A word problem framed and solved
- Framing the equations from words
- What two lines can do
- They cross once
- They never cross
- Terms in this chapter
- 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 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.