PPT: Pair of Linear Equations in Two Variables

 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