How it works
Enter each equation in the form ax + by = c. The solution is the point (x, y) that satisfies both, which is where the two lines cross.
The calculator uses Cramer's rule. If the determinant a₁b₂ − a₂b₁ is zero, the lines are parallel (no solution) or identical (infinitely many solutions).
Formula
x = (c₁b₂ − c₂b₁) ÷ (a₁b₂ − a₂b₁); y = (a₁c₂ − a₂c₁) ÷ (a₁b₂ − a₂b₁)
Questions people ask
How do I enter y = 2x + 1?
Rearrange it to ax + by = c: −2x + y = 1, so a = −2, b = 1, c = 1.
What other methods solve a 2×2 system?
Substitution (solve one equation for a variable and plug into the other) and elimination (add multiples of the equations to cancel a variable). All give the same answer.
How can a system have no solution?
If the lines have the same slope but different intercepts, they are parallel and never meet. Example: x + y = 1 and x + y = 3.