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,📘 Chapter 1: Linear
Equations in Two
Variables
🔹 What is a Linear Equation?
A linear equation in two variables is an equation of
the form:
[ax + by + c = 0]
where a, b, and c are real numbers, and x, y are
variables.
🔹 Graphical Representation
When you draw the graph of a linear equation, it
will always be a straight line.
If you plot two such equations on the same graph,
the point where they meet (intersect) is the
solution.
🔹 Types of Solutions:
1. Unique Solution
Lines intersect at one point
2
, [Consistent and Independent]
2. No Solution
Lines are parallel, never meet
[Inconsistent]
3. Infinite Solutions
Lines lie on top of each other
[Consistent and Dependent]
🔹 Methods of Solving
1. Substitution Method
Solve one equation for x or y
Substitute into the second equation
2. Elimination Method
Multiply equations to make one variable same
Subtract or add equations to eliminate one
variable
3. Cross-Multiplication Method
Use the formula:
[x / (b₁c₂ – b₂c₁) = y / (c₁a₂ – c₂a₁) = 1 / (a₁b₂
– a₂b₁)]
3
,📘 Chapter 1: Linear
Equations in Two
Variables
🔹 What is a Linear Equation?
A linear equation in two variables is an equation of
the form:
[ax + by + c = 0]
where a, b, and c are real numbers, and x, y are
variables.
🔹 Graphical Representation
When you draw the graph of a linear equation, it
will always be a straight line.
If you plot two such equations on the same graph,
the point where they meet (intersect) is the
solution.
🔹 Types of Solutions:
1. Unique Solution
Lines intersect at one point
2
, [Consistent and Independent]
2. No Solution
Lines are parallel, never meet
[Inconsistent]
3. Infinite Solutions
Lines lie on top of each other
[Consistent and Dependent]
🔹 Methods of Solving
1. Substitution Method
Solve one equation for x or y
Substitute into the second equation
2. Elimination Method
Multiply equations to make one variable same
Subtract or add equations to eliminate one
variable
3. Cross-Multiplication Method
Use the formula:
[x / (b₁c₂ – b₂c₁) = y / (c₁a₂ – c₂a₁) = 1 / (a₁b₂
– a₂b₁)]
3
