Thread: system

Solve the system:

$\displaystyle 2x-6y=-5$
$\displaystyle -3x+9y=6$



I'm trying to learn this on my own, and I know the answer to this problem is "none" ... but can someone tell me how I figure that?

And, what exactly does it mean by "solve the system" ?

Originally Posted by toop

Solve the system:

$\displaystyle 2x-6y=-5$
$\displaystyle -3x+9y=6$



I'm trying to learn this on my own, and I know the answer to this problem is "none" ... but can someone tell me how I figure that?

And, what exactly does it mean by "solve the system" ?

you post it in algebra, so i think you need to find the values of x and y. but i think you're in the wrong section.

Originally Posted by toop

Solve the system:

$\displaystyle 2x-6y=-5$
$\displaystyle -3x+9y=6$



I'm trying to learn this on my own, and I know the answer to this problem is "none" ... but can someone tell me how I figure that?

And, what exactly does it mean by "solve the system" ?

Your system is equivalent to $\displaystyle \left\{\begin{array}{rcrcr}x&-&3y&=&-\tfrac{5}{2}\\x&-&3y&=&-2\end{array}\right.$

This implies that $\displaystyle -\tfrac{5}{2}=-2$ which is false. Thus, the system is inconsistent and has no solution.

Does this make sense?

Originally Posted by toop

I know the answer to this problem is "none" ... but can someone tell me how I figure that? And, what exactly does it mean by "solve the system" ?

To "solve the system" is to find the values of x and y by any of various methods: graphing, substitution, addition / elimination, matrices, Cramer's Rule, etc.

The "none" solution means that there is no set of values for x and y that would make both equations true at the same time. If you try to solve the system by whatever method, you will end up with a nonsensical result, such as "2 = 0".

Have fun!