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 Page 1


PAIR OF LINEAR
EQUATIONS IN TWO
VARIABLES
CLASS 10
Page 2


PAIR OF LINEAR
EQUATIONS IN TWO
VARIABLES
CLASS 10
Linear equations are used to represent situations with an
unknown value. We use linear equations in various real-life
situations, such as:
Predicting weather
Budgeting expenses
Calculating ingredients for recipes
Predicting profits in business
Analyzing government surveys
Page 3


PAIR OF LINEAR
EQUATIONS IN TWO
VARIABLES
CLASS 10
Linear equations are used to represent situations with an
unknown value. We use linear equations in various real-life
situations, such as:
Predicting weather
Budgeting expenses
Calculating ingredients for recipes
Predicting profits in business
Analyzing government surveys
The general form of a linear equation in two variables is:
where a and b cannot be zero at the same time.
Example:
x + 3y = 7
ax + by + c = 0
Various Forms of Linear Equations
Page 4


PAIR OF LINEAR
EQUATIONS IN TWO
VARIABLES
CLASS 10
Linear equations are used to represent situations with an
unknown value. We use linear equations in various real-life
situations, such as:
Predicting weather
Budgeting expenses
Calculating ingredients for recipes
Predicting profits in business
Analyzing government surveys
The general form of a linear equation in two variables is:
where a and b cannot be zero at the same time.
Example:
x + 3y = 7
ax + by + c = 0
Various Forms of Linear Equations
The general form for a pair of linear equations in two
variables x and y is:
a1x + b1y + c1 = 0
a2x + b2y + c2 = 0
Pair of Linear Equations in Two Variables
Page 5


PAIR OF LINEAR
EQUATIONS IN TWO
VARIABLES
CLASS 10
Linear equations are used to represent situations with an
unknown value. We use linear equations in various real-life
situations, such as:
Predicting weather
Budgeting expenses
Calculating ingredients for recipes
Predicting profits in business
Analyzing government surveys
The general form of a linear equation in two variables is:
where a and b cannot be zero at the same time.
Example:
x + 3y = 7
ax + by + c = 0
Various Forms of Linear Equations
The general form for a pair of linear equations in two
variables x and y is:
a1x + b1y + c1 = 0
a2x + b2y + c2 = 0
Pair of Linear Equations in Two Variables
Unique Solution:
When the two equations represent two distinct lines that intersect
at a single point.
The lines are not parallel and not the same line.
Infinitely Many Solutions:
If the two linear equations represent the same line.
Every point on the line satisfies both equations.
No Solution:
When the two equations represent parallel lines that do not
intersect.
The lines have the same slope but different y-intercepts.
Types of Solutions
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FAQs on PPT: Pair of Linear Equations in Two Variables - Mathematics (Maths) Class 10

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 that contain two variables and can be represented graphically as two lines on a coordinate plane.
2. How can a pair of linear equations in two variables be solved?
Ans. A pair of linear equations in two variables can be solved using methods such as substitution, elimination, or graphing to find the values of the variables that satisfy both equations simultaneously.
3. What is the significance of finding the solution to a pair of linear equations in two variables?
Ans. The solution to a pair of linear equations in two variables represents the point of intersection of the two lines on the coordinate plane, indicating where the two equations are true at the same time.
4. Can a pair of linear equations in two variables have more than one solution?
Ans. A pair of linear equations in two variables can have one unique solution, no solution (parallel lines), or infinite solutions (coincident lines) depending on the relationship between the two equations.
5. How are pair of linear equations in two variables used in real-life applications?
Ans. Pair of linear equations in two variables are commonly used in various real-life situations such as solving problems related to cost and revenue, distance and speed, mixture and investment, and more to make informed decisions.
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