Question

​z+w−3 ​6z−10w ​​ ​=k ​=8 ​​ consider the system of equations above, where kkk is a constant. for which value of kkk are there infinitely many (w, z)(w,z)left parenthesis, w, comma, z, right parenthesis solutions?

Answer 1

Our system is the following :
$z+w-3=k\\ 6z-10w=k,\\\text{Solve the first equation for z like this:} \\z=k-w+3\\\text{Substitute in the second equation like this:}\\6(k-w+3)-10w=k\\6k-16w+18=k\\16w=6k+18-k\\w=\frac{1}{16}(6k+18-k)$

As you see, the system has only one solution whenever the value of k is. Unlike you have not well written the system.