Linear Equations in Two Variables — Class 10 Maharashtra SSC Mathematics revision notes
A 4-page visual revision sheet for Linear Equations in Two Variables, written for Class 10 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
two equations, two unknowns, and four routes to the pair that satisfies both
- One equation: endlessly many solutions, a whole line of them
- A second equation: a second line, cutting across the first
- The solution: the one pair lying on both lines at once
The standard form and what it means
- the standard form is ax + by + c = 0, with a and b not both zero and each variable to the first power only
- a solution is an ordered pair (x, y) that makes the equation true, and one equation has infinitely many
- drawing the pairs of one equation gives a straight line, which is where the word linear comes from
- two equations taken together form a simultaneous pair, and solving them means finding the pair satisfying both
- geometrically that is the point where the two lines meet, so the algebra and the picture are the same question
Four ways to solve a pair
- Elimination: multiply one or both equations so a variable has the same coefficient, then add or subtract to remove it. Usually the fastest, especially when coefficients are small
- Substitution: make one variable the subject of one equation and put that expression into the other. Best when a coefficient is already 1
- Cross multiplication: apply the formula to a, b and c directly. Quick when the numbers are awkward, but the arrangement must be exact or every term goes wrong
- Graphical: plot both lines and read off the crossing. Asked for by name, and it is the only method that shows why a pair may have no solution or infinitely many
Page 1 of 4. The full sheet, all 4 pages, opens free in the app.
What this Linear Equations in Two Variables sheet covers
- One equation
- A second equation
- The solution
- Simultaneous equations
- Linear equation in two variables
- The standard form and what it means
- Substitution method
- Elimination method
- Cross multiplication method
- Graphical method
- Four ways to solve a pair
- Elimination
- Substitution
- Cross multiplication
- Graphical
- Elimination, step by step
- Deciding to add or to subtract
- Cross multiplication, and the ratio test
- for a_1x + b_1y + c_1 = 0 and a_2x + b_2y + c_2 = 0
- a unique solution, the lines cross once
- no solution, the lines are parallel
- infinitely many, the lines coincide
- What the two lines can do
- They cross
- They do not
- Word problems on simultaneous equations
- Applications
- Word problems, and the usual shapes
- A digits problem
- 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.