Arithmetic
Additive Identity
Arithmetic Progression
Associative Property
Averages
Brackets
Closure Property
Commutative Property
Conversion of Measurement Units
Cube Root
Decimal
Distributivity of Multiplication over Addition
Divisibility Principles
Equality
Exponents
Factors
Fractions
Fundamental Operations
H.C.F / G.C.D
Integers
L.C.M
Multiples
Multiplicative Identity
Multiplicative Inverse
Numbers
Percentages
Profit and Loss
Ratio and Proportion
Simple Interest
Square Root
Unitary Method
Algebra
Cartesian System
Order Relation
Polynomials
Probability
Standard Identities & their applications
Transpose
Geometry
Basic Geometrical Terms
Circle
Curves
Angles
Define Line, Line Segment and Rays
Non-Collinear Points
Parallelogram
Rectangle
Rhombus
Square
Three dimensional object
Trapezium
Triangle
Quadrilateral
Trigonometry
Trigonometry Ratios
Data-Handling
Arithmetic Mean
Frequency Distribution Table
Graphs
Median
Mode
Range

Videos
Solved Problems
Home >> Polynomials >> Linear Equations >> Linear Equation in Two Variables >>

Linear Equation in Two Variables

Linear Equation in one Variable Linear Equation in Two Variables Difference between Linear Equation in One & Two Variables Linear Expression Linear Equations Complex Examples
Solving a Pair of Linear Equations

Before you understand Linear Equation in Two Variables, you are advised to read:

What is Linear Equations in One Variable ?

What is Linear Equations in Two Variables

Linear Equations which are written in the form of; ax + by + c = 0,
Where a, b, c are real numbers and a, b, c are both not equal to Zero. Such Linear Equations are known as Linear Equations in Two Variables.

Example: In a cricket match, batsman 1 & batsman 2 together scored 100 runs. Express this in the form of linear equation:
Solution: As per the question:
Let Batsman 1 = a
Batsman 2 = b

Since both batsmen together scored 100 runs, so we get:
a + b = 100

or we can also write it as:
a + b - 100 = 0

And you can see that the above equation is in the form of ax + by + c = 0, Hence, this forms a linear equation in two variables.

Solving Linear Equations in Two Variables

As we know that Linear Equations with two variables are written in the form of; ax + by + c = 0, So, we get the solution when we find the values of both variables i.e. x and y.

Unlike, Linear Equation in One variable which has a unique solution; linear equation in two variable has infinitely many solution.

Example: x + y = 15
In the given linear equation with two variable x and y, we can have following multiple solutions:

Solution 1: If x = 0, then we get:
0 + y = 15
Or
y = 15
So, x = 0 & y = 15 and solution of linear equation is (0 , 15)

Solution 2: If x = 2, then we get:
2 + y = 15
Subtract 2 from both sides and we get:
y = 13
So, x = 2 & y = 13 and solution of linear equation is (2 , 13)

Solution 3: If y = 3, then we get:
x + 3 = 15
Subtract 3 from both sides and we get:
x = 12
So, x = 12 & y = 3 and solution of linear equation is (12 , 3)

Solution 4: If y = 5, then we get:
x + 5 = 15
Subtract 5 from both sides and we get:
x = 10
So, x = 10 & y = 5 and solution of linear equation is (10 , 5)

From the above solution 1, 2, 3 & 4 you can observe that linear equation in two variables has infinitely many solutions.
Also, note that while writing the solution, first write the value of x and then the value of y.

Copyright@2022 Algebraden.com (Math, Algebra & Geometry tutorials for school and home education)