PPT: Pair of Linear Equations in Two Variables

# Pair of Linear Equations in Two Variables Class 6 PPT

``` Page 2

WHAT IS LINEAR EQUATION?
An equation between two variables
that gives a straight line when
plotted on a graph.
Page 3

WHAT IS LINEAR EQUATION?
An equation between two variables
that gives a straight line when
plotted on a graph.
WHAT IS LINEAR EQUATION IN TWO VARIABLE?
A linear equation in two variables is an equation with
two variables (usually called x and y) where the
variables are at most multiplied by a number, and
added to something else. No exponents, no variables in
denominators, no fancy functions of the variables.
For example 2x-y=3 and x+y=3 are linear equations.
Page 4

WHAT IS LINEAR EQUATION?
An equation between two variables
that gives a straight line when
plotted on a graph.
WHAT IS LINEAR EQUATION IN TWO VARIABLE?
A linear equation in two variables is an equation with
two variables (usually called x and y) where the
variables are at most multiplied by a number, and
added to something else. No exponents, no variables in
denominators, no fancy functions of the variables.
For example 2x-y=3 and x+y=3 are linear equations.
GRAPH OF LINEAR EQUATION IN TWO VARIABLE
Page 5

WHAT IS LINEAR EQUATION?
An equation between two variables
that gives a straight line when
plotted on a graph.
WHAT IS LINEAR EQUATION IN TWO VARIABLE?
A linear equation in two variables is an equation with
two variables (usually called x and y) where the
variables are at most multiplied by a number, and
added to something else. No exponents, no variables in
denominators, no fancy functions of the variables.
For example 2x-y=3 and x+y=3 are linear equations.
GRAPH OF LINEAR EQUATION IN TWO VARIABLE
TYPES OF SOLUTIONS OF SYSTEMS OF EQUATIONS
• One solution – the lines cross at one point
• No solution – the lines do not cross
• Infinitely many solutions – the lines coincide
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## Mathematics (Maths) Class 10

118 videos|463 docs|105 tests

## FAQs on Pair of Linear Equations in Two Variables Class 6 PPT

 1. What is a pair of linear equations in two variables?
Ans. A pair of linear equations in two variables is a set of two equations with two variables, typically represented as x and y, where each equation is of the form ax + by = c, and a, b, and c are real numbers.
 2. How can we solve a pair of linear equations in two variables?
Ans. There are several methods to solve a pair of linear equations in two variables. The most commonly used methods are substitution method, elimination method, and graphical method. These methods involve manipulating the equations to eliminate one variable and find the values of the remaining variables.
 3. What is the significance of solving a pair of linear equations in two variables?
Ans. Solving a pair of linear equations in two variables helps in finding the common solution, if any, that satisfies both equations simultaneously. These solutions represent the point of intersection of the two lines represented by the equations on a Cartesian plane. It is useful in various real-life scenarios, such as solving problems related to cost and revenue, distance and speed, and supply and demand.
 4. Can a pair of linear equations in two variables have no solution?
Ans. Yes, a pair of linear equations in two variables can have no solution. This happens when the lines represented by the equations are parallel and never intersect. In such cases, the equations are said to be inconsistent, and there is no common solution that satisfies both equations simultaneously.
 5. Can a pair of linear equations in two variables have infinitely many solutions?
Ans. Yes, a pair of linear equations in two variables can have infinitely many solutions. This happens when the lines represented by the equations are coincident or overlapping. In such cases, every point on the line is a solution to the pair of equations. The equations are said to be dependent, and any value of x or y that satisfies one equation will satisfy the other equation as well.

## Mathematics (Maths) Class 10

118 videos|463 docs|105 tests

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