Algebra
Determinant of the coefficients
Built from the four coefficients that multiply the unknowns. It appears in the denominator of both solutions, so it must be non-zero for a unique answer to exist.
The Formula
D = a1 b2 - a2 b1
Built from the four coefficients that multiply the unknowns. It appears in the denominator of both solutions, so it must be non-zero for a unique answer to exist.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| a1 | x coefficient in the first equation | dimensionless | The number multiplying x in equation one. |
| b1 | y coefficient in the first equation | dimensionless | The number multiplying y in equation one. |
| a2 | x coefficient in the second equation | dimensionless | The number multiplying x in equation two. |
| b2 | y coefficient in the second equation | dimensionless | The number multiplying y in equation two. |
| D | Determinant | dimensionless | Zero means the lines are parallel or identical. |
What Each Symbol Means
a1dimensionless
x coefficient in the first equation
The number multiplying x in equation one.
b1dimensionless
y coefficient in the first equation
The number multiplying y in equation one.
a2dimensionless
x coefficient in the second equation
The number multiplying x in equation two.
b2dimensionless
y coefficient in the second equation
The number multiplying y in equation two.
Ddimensionless
Determinant
Zero means the lines are parallel or identical.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to solve a system of linear equations page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Solve A System Of Linear Equations, filed under Math. Every number the guide produces comes from substituting into this one line.