Algebra Solving Methods
Linear: ax + b = c → x = (c − b) / a
System (Substitution or Elimination):
a₁x + b₁y = c₁
a₂x + b₂y = c₂
Determinant D = a₁×b₂ − a₂×b₁
x = (c₁×b₂ − c₂×b₁) / D
y = (a₁×c₂ − a₂×c₁) / D
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Equation Solver
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Frequently Asked Questions
What if a = 0 in a linear equation?
If a = 0, there's no variable x. The equation becomes b = c. If b = c, any value of x satisfies it (infinite solutions). If b ≠ c, no value of x satisfies it (no solution). These are degenerate cases — the equation is not truly linear.
What if the determinant is 0 in a system?
If the determinant D = 0, the two equations are either parallel lines (no solution) or the same line (infinite solutions). This means the system is either inconsistent or dependent. You cannot solve for unique x and y values when D = 0.