Question 656167
No solution means the lines are {{{parallel}}}. 

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

{{{4x+ky=5}}}

The left hand sides are multiples of each other.

Find the multiplier {{{M}}} so that,

{{{M(2x-y)=4x+ky}}}

{{{2Mx-My=4x+ky}}}

Solve for the {{{x}}} and {{{y}}} terms on both sides.

{{{2Mx=4x}}}...{{{2M=4}}}...->...{{{M=2}}}

{{{-My=ky}}}...->... {{{-M=k}}} ...->...{{{k=-2}}}


{{{highlight(k=-2)}}}


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

{{{4x+(-2)y=5}}}
------------------

{{{2x-y=3}}}.....->{{{2x-3=y}}}

{{{4x-2y=5}}}....->{{{2x-2/5=y}}}



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