Algebra
Solution for y
This time the constants replace the y coefficients and the x coefficients stay. The pattern mirrors the formula for x.
The Formula
y = (a1 c2 - a2 c1) / D
This time the constants replace the y coefficients and the x coefficients stay. The pattern mirrors the formula for x.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| a1 | x coefficient in the first equation | dimensionless | Unchanged from the determinant. |
| a2 | x coefficient in the second equation | dimensionless | Unchanged from the determinant. |
| c1 | Constant in the first equation | dimensionless | Substituted in place of the y coefficient. |
| c2 | Constant in the second equation | dimensionless | Substituted in place of the y coefficient. |
| D | Determinant | dimensionless | The same value used for x. |
What Each Symbol Means
a1dimensionless
x coefficient in the first equation
Unchanged from the determinant.
a2dimensionless
x coefficient in the second equation
Unchanged from the determinant.
c1dimensionless
Constant in the first equation
Substituted in place of the y coefficient.
c2dimensionless
Constant in the second equation
Substituted in place of the y coefficient.
Ddimensionless
Determinant
The same value used for x.
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.