Author: Kaviya S STD 10
- Topic tree
- TDS – Terms Definition and Symbols
- DEF – Data, Equations and Formulae
- Infographics
- Concept maps / Model Problem Mapping / Sketch Note
- Question bank
- Guided Practice
- Quiz
- Key for Quiz
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Topic Tree
- Pair Of Linear In Two Variable
- Graphical Method Of Solution Of A Pair Of Linear Equations
- Algebraic Methods Of Solving A Pair Of Linear Equations
- Substitution Method
- Elimination Method
- Cross Multiplication Method
- Equation Reducible to a Pair of linear equations in two variables
- Word Problems
Terms, Definitions and Symbols
Equation: An algebraic expression with ‘equal’ to sign ,i.e. (=) is called an equation.
Ex: 6x+12=0,7x+28=0 etc…
Linear equation in one variable: An equation which involves only one variable with highest power 1,is called a linear equation in one variable
Linear equation in two variable: An equation which involves two variables with highest power 2,is called a linear equation in two variables
Pair of linear equations in two variable: If two linear equations have the two same variables, they are called a pair of linear equations in two variables.
General form of pair of linear equations: a1x + b1y + c1 = 0,a2x + b2y + c2 = 0.or ax + by=c
Graphical representation: The graph of every linear equation in two variables is a straight line. a pair of linear equations in two variables will be represented by two straight lines.
Algebraic representation: The representation of word problem in the form of linear equations is called its algebraic representation.
Solutions of pair of linear equations in two variables : Any pair of values of x and y which satisfies both the equations, a1x + b1y + c1 = 0,a2x + b2y + c2 = 0 ,is called a solution of given pair of linear equation.
A pair of linear equations in two variables can be solved by two methods namely Graphical method and Algebraic method.
Graphical method: The graph of a pair of linear equations in two variables is presented by two lines. To find a solution graphically ,first draw the graph of both equations on the same graph with same scale of representation.
- Intersecting lines
- Coincident lines
- Parallel lines
Algebraic method: The graphical method is suitable for integer solutions but it cannot be suitable for non-integer solutions, since it may not be accurate as needed. So, there are several algebraic methods, which can also be used for solving a pair of linear equations.
Methods for solving a pair of linear equations using algebraic method are:
- Substitution method
- Elimination method
- Cross-multiplication method.
Consistent system: A system of linear equations is said to be consistent if it has at least one solution.
Inconsistent system: A system of linear equations is said to be inconsistent if it has no solution.
