Substitution Calculator

Substitution Calculator

Select the equation number and enter all coefficients and constant values to simplify the linear equation.

Calculation For:

a₁

b₁

k₁

a₂

b₂

k₂

a₁

b₁

c₁

k₁

a₂

b₂

c₂

k₂

a₃

b₃

c₃

k₃

a₁ x + b₁y = k₁

a₂ x + b₂y = k₂

a₁ x + b₁y + c₁z = k₁

a₂ x + b₂y + c₂z = k₂

a₃ x + b₃y + c₃z = k₃

Substitution Method Calculator

The Substitution Method Calculator simplifies solving algebraic equations by substituting one variable into another equation. This allows you to find the values of all variables efficiently.

What is the Substitution Method?

The substitution method is an algebraic process where the value of one variable from one equation is substituted into another equation to find all variable values. It is commonly used for solving systems of linear equations.

Types of Substitution Methods

Algebraic Method: Solve equations using algebraic manipulation.
Graphical Method: Solve equations by plotting lines and finding intersection points.

Steps for Substitution Method

Solve one equation for one variable.
Substitute this variable into the second equation.
Solve the resulting equation to find the values of all variables.

Example:

Solve the system of equations:

Eq1: 2x + 4y = 4

Eq2: x + y = 3

From Eq2: x = 3 - y
Substitute x in Eq1: 2(3 - y) + 4y = 4
Solve for y: 6 - 2y + 4y = 4 → 2y = -2 → y = -1
Substitute y back in Eq2: x + (-1) = 3 → x = 4

Solution: x = 4, y = -1

Other Examples:

System of Equations	Solution
x + y = 5 ; x + 2y = 7	x = 3, y = 2
-x - 7y = -1 ; x - 2y = -8	x = -6, y = 1
2x + y = 7 ; 3x - 4y = 1	x = 38/11, y = 1/11
2x - y = 3 ; x + 2y = 2	x = 8/5, y = 1/5
x - 3y = -43 ; 2x + 2y = -41	x = -209/8, y = 45/8

How to Use the Substitution Calculator

Input:

Enter the variables (x and y) in the designated fields.
Enter the constant values for each equation.
Click "Calculate" to solve.

Output:

Values of x and y.
Step-by-step solution process for clarity.

FAQs

Why use the substitution method?

The substitution method provides a clear and simple way to solve a system of linear equations. The calculator shows all steps, making it easy to understand and verify the solution.

References

Wikipedia: Substitution (Logic)
Calc-Workshop: Algebra Substitution Method