Variables: Find values so system has no soln, one soln, or

[chargers_999]

I have been trying to figure out this problem for a long time. The problem is:


Using the variables state the conditions that make the system below have 1. No solution 2. Infinite solutions or 3. One solution
cx+dy=e
fx+gy=f

I have been trying to find values that make the problems work but don't know what to do

Thank You,
Larry

 

[tkhunny]

"Real" Numbers, right?

This is a definition and understanding problem. It is NOT a calculating problem. If you are unable to get any of the three requests, you simply must go back and review the materials again. You are missing something significant.

No Solution:

Pick any 4 values such that c*g - f*d = 0. ANY 4 values with this property. It doesn't even matter what e and f are.

Lot's of solutions:

Pick just about anything for c, d, and e
Then pick f = k*c, g = k*d, and f = k*e where k is some other number.

Only one solution:

Pick any six values that fall into neither of the previous two classifications.

 

[stapel]

Think about the various systems you have solved. For instance, what sort of solution would the following system have?

. . . . .\(\displaystyle \L \begin{array}{rrrcr}x&+&y&=&3\\2x&+&2x&=&6 \end{array}\)

How about the following system?

. . . . .\(\displaystyle \L \begin{array}{rrrcr}x&+&y&=&3\\2x&+&2x&=&5 \end{array}\)

Or this one?

. . . . .\(\displaystyle \L \begin{array}{rrrcr}x&+&y&=&3\\2x&-&y&=&3 \end{array}\)

How can you tell?

Now think about the (symbolic) system they've given you. What can you do to rearrange the system into something you can interpret in a manner similar to the ones above?

Eliz.

P.S. Welcome to FreeMathHelp!

 

[tkhunny]

P.S. Welcome to FreeMathHelp!

Right. I didn't check that. Sorry if I beat you up a little on your first try.