Solve Equations Using Substitution Elimination

Linear Equation System:

\[ \begin{cases} a_1x + b_1y = c_1 \\ a_2x + b_2y = c_2 \end{cases} \]

First equation (x coefficient):

First equation (y coefficient):

First equation (constant):

Second equation (x coefficient):

Second equation (y coefficient):

Second equation (constant):

Method:

Solution:

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1. What Is Substitution Elimination Method?

The substitution and elimination methods are algebraic techniques for solving systems of linear equations. Substitution involves solving one equation for a variable and substituting into the other, while elimination adds or subtracts equations to eliminate a variable.

2. How Does the Calculator Work?

The calculator solves systems of two linear equations:

\[ \begin{cases} a_1x + b_1y = c_1 \\ a_2x + b_2y = c_2 \end{cases} \]

Using either:

Substitution: Solve one equation for one variable and substitute into the other
Elimination: Multiply equations to align coefficients, then add/subtract to eliminate a variable

3. When to Use Each Method

Substitution is often easier when one equation is already solved for a variable. Elimination works better when coefficients are easily aligned.

4. Using the Calculator

Tips: Enter all coefficients and constants. Select your preferred method. The calculator will show step-by-step solution or indicate if no unique solution exists.

5. Frequently Asked Questions (FAQ)

Q1: What if the system has no solution?
A: The calculator will indicate if the lines are parallel (no solution) or coincident (infinite solutions).

Q2: Can this solve non-linear equations?
A: No, this calculator is designed only for linear equation systems.

Q3: How accurate are the solutions?
A: Solutions are calculated with 4 decimal places precision.

Q4: Can I solve larger systems?
A: This calculator handles 2-variable systems. For larger systems, matrix methods are needed.

Q5: Which method is better?
A: It depends on the specific equations. Substitution may be simpler when one variable has coefficient 1.