Originally Posted by

**Dark Sun** Peter, subtract the two equations to get:

$\displaystyle -2b+5c=0\Rightarrow 5c=2b$

Then, all points along this line will satisfy the system. Select $\displaystyle c=-4$.

Which gives us: $\displaystyle 2b=5(-4)=-20\Rightarrow b=-10$

Then, plug these two results into our first equation, to get:

$\displaystyle 0=-2a+3b+9c=-2a+3(-10)+9(-4)=-2a-30-36\Rightarrow 66=-2a\Rightarrow -33=a$

To give us a final result of $\displaystyle (-33,-10,-4)$.

This is not the only correct answer for this system. Hope this helps, thanks!