Question 985240
<pre>
A system of equations is consistent and independent if and only if 
the matrix of coefficients is non-singular, which is the same as saying
the determinant of the matrix of coefficients is not 0.  The two systems
have the same coeficient matrices.  Thus the answer is yes. 


The solutions to the first system 

ax+by=c
dx+ey=f

is

{{{x}}}{{{""=""}}}{{{(ce-bf)/(ae-bd)}}}
{{{y}}}{{{""=""}}}{{{(af-cd)/(ae-bd)}}}

And since it is a consistent and independent system, the denominator ae-bd
is not 0.

The solutions to the second system

ax+by=g
dx+ey=h

 is

{{{x}}}{{{""=""}}}{{{(ge-bh)/(ae-bd)}}}
{{{y}}}{{{""=""}}}{{{(ah-gd)/(ae-bd)}}}

the denominator ae-bd is not 0.

So the answer is yes.

Edwin</pre>