System of two linear equations solver
Cramer's rule turns a 2x2 system into three determinants, and the answer is exact when the inputs are.
x
3
- y
- 2
- Determinant Zero means the lines are parallel or identical.
- -14
- Has a unique solution
- 1
Show the working
- a1 (coefficient of x, first equation) = 2
- b1 (coefficient of y, first equation) = 3
- c1 (right-hand side, first equation) = 12
- a2 (coefficient of x, second equation) = 4
- b2 (coefficient of y, second equation) = -1
- c2 (right-hand side, second equation) = 10
- Determinant = 2*-1 - 4*3 = -14
- det_x = 12*-1 - 10*3 = -42
- det_y = 2*10 - 4*12 = -28
- x = -14 != 0 ? -42 / -14 : 0 = 3
- y = -14 != 0 ? -28 / -14 : 0 = 2
- Has a unique solution = -14 != 0 ? 1 : 0 = 1
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- D = a1 b2 - a2 b1
- x = (c1 b2 - c2 b1) / D
- y = (a1 c2 - a2 c1) / D