for what value of k does the linear system have no solution?
2x+ky=11
3x-y=11

Question

for what value of k does the linear system have no solution?
2x+ky=11
3x-y=11

callisto · Answer

If it has no solution , the two lines must be // => they have same slope
So -2/k = -(3/-1)
Can you solve it?

callisto · Answer

// is parallel :S

anonymous · Answer

sorry i still don't get it

callisto · Answer

I don't know if you know it...For equation having the form Ax+By+C=0 , slope = -A/B

callisto · Answer

Ahh... slow motion ..
First, if they have solution, they should intersect, agree?

anonymous · Answer

yes

anonymous · Answer

i have to go right now sorry!!!!

callisto · Answer

:O.... what should I do.... I would explain here. When you come back take a look at it. See if you understand. If not, please ask..

anonymous · Answer

Remember this property:

A linear system:

 ax+by=c
 lx+my=k

has no solution when

$$\frac a l = \frac b m \neq \frac c k $$

The system is also referred to as inconsistent.

Revert if you need a proof.

callisto · Answer

In your question, it says 'no solution'. Then, the 2 lines you have should not intersect. You also need to know that parallel lines do not intersect. like this: |dw:1335712305206:dw|
So, for your question, the 2 lines should be parallel. 
Parallel lines have the same slope. 
Next, you need to find out the slope of the line and compare them. Then, write them into an equation and solve it.(since the slopes are equal)
To get the slope, you can use the above method or rewrite the equation into slope-intersect form.
Hope you get it.

anonymous · Answer

The above reasoning only works because we can metamorphose a linear equation of two variable into a equation of straight line. For systems of higher order this may not be the right way to illustrate inconsistency.