Solve a system of two linear equations in two unknowns. Enter the coefficients for both equations.
Solution (x, y)
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Where the lines cross.Usage Tip
Two lines either cross once (one solution), run parallel (none), or coincide (infinitely many) — the determinant tells which.
THE MATH
a1·x + b1·y = c1 and a2·x + b2·y = c2
Solved by Cramer rule using the determinant a1·b2 − a2·b1
Solved by Cramer rule using the determinant a1·b2 − a2·b1
A system of two linear equations represents two lines; the solution is where they intersect.
If the determinant is zero, the lines are parallel or identical and there is no single solution.
If the determinant is zero, the lines are parallel or identical and there is no single solution.
Enter the equations in the form ax + by = c.
A non-zero determinant gives one unique solution.
Zero determinant means no solution or infinitely many.
A non-zero determinant gives one unique solution.
Zero determinant means no solution or infinitely many.