The function matches to parts of the matrix equation, using the named formats with row names and solves the matrix equation.

## Details

This function is used in wrapper functions, such as `multiplier_create`

.
to solve particular problems, but it can be used directly, too.
The function only performs the lhs
pairing industries and checking for exceptions.

## Examples

```
Im = data.frame (
a = c("row1", "row2"),
b = c(1,1),
c = c(2,0))
LHS = data.frame (
a = "lhs",
b = 1,
c = 0.5)
equation_solve (Im = Im, LHS = LHS)
#> b c
#> [1,] 1.5 2
```