CBSE Class 10 Maths Formulas from Chapter 3 - Pair of Linear Equations in Two Variables are provided here. Along with the formulas you can also get to read all necessary definitions and properties occurring in the chapter. Thus, by going through this chapter, you may easily revise all formulas and properties related to the system of linear equations and become efficient to solve the problems based on a pair of linear equations.
Check all formulas below:
1. Linear Equation: An equation which can be put in the form ax + by + c = 0, where a, b and c are Pair of Linear Equations in Two Variables, and a and b are not both zero, is called a linear equation in two variables x and y
2. Solution of system of linear equations: The value of x and y that satisfies each one of the equations in the given pair of linear equations is called solution of the given system.
3. Consistent system of linear equations: A system of linear equations is said to be consistent, if it has at least one solution.
4. Inconsistent system of linear equation: A system of linear equations is said to be inconsistent, if it has no solution.
Also Check: CBSE Class 10 Maths Syllabus 2021-2022
5. Graphical Method to Solve a Pair of Linear Equations
Let a pair of linear equations be represented as:
a_{1}x + b_{1}y + c_{1} = 0
and a_{2}x + b_{2}y + c_{2} = 0
Then the set of solutions for both equations can be determined as follows:
Compare the Ratios |
Graphical Representation |
Algebraic Interpretation |
a_{1}/a_{2} ≠ b_{1}/b_{2} |
Intersecting lines |
Exactly one or unique solution |
a_{1}/a_{2} = b_{1}/b_{2} = c_{1}/c_{2} |
Coincident lines |
Infinitely many solutions |
a_{1}/a_{2} = b_{1}/b_{2} ≠ c_{1}/c_{2} |
Parallel lines |
No solution |
The graph of a pair of linear equations in two variables is represented by two lines.
(i) If the lines intersect at a point, then that point gives the unique solution of the two equations. In this case, the pair of equations is consistent.
(ii) If the lines coincide, then there are infinitely many solutions - each point on the line being a solution. In this case, the pair of equations is dependent (consistent).
(iii) If the lines are parallel, then the pair of equations has no solution. In this case, the pair of equations is inconsistent
6. Algebraic Method to Solve a Pair of Linear Equations:
There are three methods to solve a pair of linear equations:
(i) Substitution Method
(ii) Elimination Method
(iii) Cross-multiplication Method
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