Algebra
Solution for x
The constants replace the x coefficients in the numerator, while the y coefficients stay in place. Divide by the determinant to get x.
The Formula
x = (c1 b2 - c2 b1) / D
The constants replace the x coefficients in the numerator, while the y coefficients stay in place. Divide by the determinant to get x.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| c1 | Constant in the first equation | dimensionless | The right hand side of equation one. |
| c2 | Constant in the second equation | dimensionless | The right hand side of equation two. |
| b1 | y coefficient in the first equation | dimensionless | Unchanged from the determinant. |
| b2 | y coefficient in the second equation | dimensionless | Unchanged from the determinant. |
| D | Determinant | dimensionless | Computed from the coefficients before either unknown. |
What Each Symbol Means
c1dimensionless
Constant in the first equation
The right hand side of equation one.
c2dimensionless
Constant in the second equation
The right hand side of equation two.
b1dimensionless
y coefficient in the first equation
Unchanged from the determinant.
b2dimensionless
y coefficient in the second equation
Unchanged from the determinant.
Ddimensionless
Determinant
Computed from the coefficients before either unknown.
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.