Inputs
System of Equations Solver
Enter coefficients for equations in the form ax + by = c.
Result
--
105
System of Equations Solver Calculator
Solve a 2x2 linear system in standard form and find x and y.
Sponsored
How It Works
How the System of Equations Solver Calculator works
Inputs used
Enter Equation 1 x coefficient, Equation 1 y coefficient, Equation 1 constant, Equation 2 x coefficient, Equation 2 y coefficient, and Equation 2 constant. Those values let the page solve a 2x2 linear system in standard form and find x and y.
Calculation method
This solver treats the system as two linear equations in standard form: ax + by = c.
It uses the determinant of the coefficient matrix to decide whether the system has one unique solution, infinitely many solutions, or no solution.
Determinant
\[D = a_1b_2 - a_2b_1\]
If the determinant is not zero, the system has one unique solution.
x value
\[x = \frac{c_1b_2 - c_2b_1}{D}\]
This is Cramer's rule for the x-coordinate of the solution.
y value
\[y = \frac{a_1c_2 - a_2c_1}{D}\]
This is Cramer's rule for the y-coordinate of the solution.
What the result means
The main result shown here is solution. The calculator also returns x value, y value, determinant, and classification so you can review the most useful supporting numbers at the same time.