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

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Answer 1 · 2015-02-04T15:43:06

The solution is: impossible.

A system written in the way:

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

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.

How do you solve the linear system of equations 5x-6y=305x−6y=305x-6y=30 and 10x-12y=1110x−12y=1110x-12y=11?