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

Feb 4, 2015

The solution is: impossible.

A system written in the way:

$a x + b y = c$
$a ' x + b ' y = c '$

if $\frac{a}{a '} \ne \frac{b}{b} '$ , than the system is possible or determinate.

If $\frac{a}{a '} = \frac{b}{b '} = \frac{c}{c '}$ the system is indeterminate (i.e. $\infty$ solutions).

If $\frac{a}{a '} = \frac{b}{b '} \ne \frac{c}{c '}$ the system is impossible (i.e. no solution).

Since $\frac{5}{10} = \frac{- 6}{-} 12 \ne \frac{30}{11}$, than the system is impossible.