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System of Equations Calculator

Solve systems of linear equations using elimination or matrix methods

Solution Method

Equation 1: a₁x + b₁y = c₁

Equation 2: a₂x + b₂y = c₂

📐Solution Methods

Elimination Method
Multiply equations to eliminate one variable
Best for simple coefficients
Matrix Method
Use determinants (Cramer's Rule)
Systematic and organized

💡Types of Solutions

One Solution
Lines intersect at one point
Consistent and independent
No Solution
Parallel lines (never intersect)
Inconsistent system
Infinite Solutions
Same line (coincident)
Consistent and dependent

💼Real-World Applications

Business
• Supply and demand
• Cost optimization
• Break-even analysis
Engineering
• Circuit analysis
• Structural loads
• Network flow
Science
• Chemical mixtures
• Physics problems
• Rate problems

System of Equations Calculator