Question 649252
Now we want a system with no solutions. This mean the slopes are the same, 
but the y-intercepts are different,the lines are parallel . Again, let's get these into slop-intercept form. 
{{{2x-y =5}}}....->...{{{y=2x-5}}} 
{{{6x+ky=2}}}...->....{{{y=-(6/k)x+2/k}}}

Again, we set the slopes equal to each other. This gives us 2 = -(6/k). 
{{{2k = -6}}}
{{{k = -6/2}}}
{{{highlight(k=-3)}}}

Now, we need to verify that the {{{y-intercepts}}} are not the same. 
 first substitute {{{k}}} in {{{y=-(6/k)x+2/k}}}

{{{y=-(6/-3)x+2/-3}}}

{{{y=2x-2/3}}}

 The first one is {{{-5}}}, and the second one is {{{2/k}}}, or {{{-2/3}}}

They clearly are not the same, so the {{{system }}}{{{has}}}{{{ no}}}{{{ solutions}}}.


.
{{{graph(600,600,-10,10,-10,10,0,2x-5,2x-2/3)}}}