Systems of Equations: Two Lines, One Meeting Point
Two equations in two unknowns usually meet at one point. Cramer's rule finds that point from the coefficients alone.
What is the System of Equations Solver?
Enter the coefficients of a1x + b1y = c1 and a2x + b2y = c2. The tool applies Cramer's rule with the determinant and shows x and y. If the determinant is zero, the lines are parallel or identical, so there is no single solution.
How to use it
- Enter the first equation's coefficients.
- Enter the second equation's coefficients.
- Click Solve System.
Worked example
For 2x + 3y = 13 and x - y = 2, the determinant is -5, giving x = 3.8 and y = 1.8.
What solves 2x + 3y = 13 and x - y = 2?
x = 3.8 and y = 1.8, since the determinant is -5 and the rule divides each numerator by it.
Frequently asked questions
What does a zero determinant mean?
The lines never meet at one point: they are parallel or the same line.
Can I check the answer?
Yes. Put x and y back into both equations; both sides must match.