Enter two linear equations in the form ax + by = c and get the solution instantly with full elimination working shown.
Equation 1: a₁x + b₁y = c₁
Equation 2: a₂x + b₂y = c₂
This calculator uses the elimination method:
What does "no solution" mean?
If the two equations represent parallel lines, they never intersect and there is no solution. This happens when the ratios of the x and y coefficients are equal but the constants are different.
What does "infinite solutions" mean?
If both equations represent the same line, every point on that line is a solution. This happens when both equations are multiples of each other.
What is the difference between elimination and substitution?
Both methods give the same answer. Elimination removes one variable by adding or subtracting equations. Substitution rearranges one equation to express one variable in terms of the other, then substitutes into the second equation. Elimination is generally quicker when coefficients are simple integers.
Can this solve three equations with three unknowns?
Not currently — this calculator handles two equations with two unknowns. Systems of three equations require matrix methods (Gaussian elimination) which is more complex.