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Math Calculators
System of Equations Calculator
Solve a system of two linear equations (a₁x + b₁y = c₁ and a₂x + b₂y = c₂) for x and y.
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About the System of Equations Calculator
A system of two linear equations can be solved using elimination (Cramer's rule), which combines the equations to cancel one variable at a time.
Formula: Given a₁x + b₁y = c₁ and a₂x + b₂y = c₂, let D = a₁b₂ − a₂b₁. Then x = (c₁b₂ − c₂b₁) ÷ D and y = (a₁c₂ − a₂c₁) ÷ D.
If D = 0, the lines are parallel and there is no unique solution. This method is widely used in algebra, economics and engineering to solve simultaneous constraints.
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