Question

How do you solve the linear system of equations `5x-6y=30` and `10x-12y=11`?

Answer 1

The solution is: impossible.

A system written in the way:

`ax+by=c`
`a'x+b'y=c'`

if `a/(a')!=b/b'` , than the system is possible or determinate.

If `a/(a')=b/(b')=c/(c')` the system is indeterminate (i.e. `oo` solutions).

If `a/(a')=b/(b')!=c/(c')` the system is impossible (i.e. no solution).

Since `5/10=(-6)/-12!=30/11`, than the system is impossible.