Question

Find conditions on k that will make the following system of equations have a unique solution. To enter your answer, first select whether k should be equal or not equal to specific values, then enter a value or a list of values separated by commas.Then give a formula in terms of k for the solution to the system, when it exists. Be sure to include parentheses where necessary, e.g. to distinguish 1/(2k) from 1/2k.3kx+3y = 43x+3ky = 1The system has a unique solution when k (equal or not equal) to ???The unique solution is x = y =

Answer 1

`k\\ot = -1,1`

`x=(4k-1)/(3(k^2-1))`

`y=(k-4)/(3(k^2-1))`

Explanation:

First we see that 3k/3 can't be equal to 3/3k, so we have

`9k^2\\ot =9`, i.e, k can't be -1 or 1.

multiple first equation with k:

`3k^2x+3ky=4k`

`3x+3ky=1`

then we have:

`3(k^2-1)x=4k-1`

i.e,

`x=(4k-1)/(3(k^2-1))`

And now we calc y:

`3k(4k-1)/(3(k^2-1))+3y=4`

`y=(k-4)/(3(k^2-1))`

for any k not eql to -1 or 1.