Substitution Method Calculator
Solve systems of linear equations using the substitution method with step-by-step solutions
System of Linear Equations
First Equation: a₁x + b₁y = c₁
Second Equation: a₂x + b₂y = c₂
Example Problems
Example 1: Simple System
System:
3x - 4y = 6
-x + 4y = 2
Solution: x = 4, y = 1.5
Example 2: No Solution
System:
2x + 3y = 7
2x + 3y = 10
Solution: No solution (inconsistent)
Substitution Method Steps
Choose equation
Select one equation to solve for a variable
Solve for variable
Express one variable in terms of the other
Substitute
Replace the variable in the other equation
Solve & verify
Find values and check by substitution
Solution Tips
Choose the equation with coefficient ±1 for easier algebra
If both variables disappear and you get 0 = 0, there are infinite solutions
If both variables disappear and you get 0 = non-zero, there's no solution
Always verify your solution in both original equations
Understanding the Substitution Method
What is the Substitution Method?
The substitution method is a technique for solving systems of linear equations by solving one equation for one variable and then substituting that expression into the other equation. This reduces the system to a single equation with one unknown.
When to Use Substitution
- •When one variable has a coefficient of ±1
- •When one equation is already solved for a variable
- •When dealing with non-linear systems
- •For educational purposes to understand solution methods
Types of Solutions
Unique Solution
System has exactly one solution (x, y) that satisfies both equations.
Infinite Solutions
Both equations represent the same line (dependent system).
No Solution
Equations represent parallel lines (inconsistent system).
General Form
a₁x + b₁y = c₁
a₂x + b₂y = c₂
where a₁, b₁, c₁, a₂, b₂, c₂ are constants