so for no solution, they need to be parallel lines, because they will never intersect
parallel lines have the exact same slope
So let's make our slope (k/coefficient of y, coefficient of x/coefficient of y) have the same ratio in both equations:
[tex]0.3x - 0.7y = 1 \\ y = \frac{ - 0.3x}{ - 0.7} - \frac{1}{2.8} \\ slope \: (m) = \frac{ - 0.3}{ - 0.7} = 0.429[/tex]
[tex]kx - 2.8y = 3 \\ y = \frac{ - kx}{ - 2.8} - \frac{3}{ 2.8} \\ slope \: (m) = \frac{ - k}{ - 2.8} .. \frac{ - k}{ - 2.8} = 0.429 [/tex]
[tex]\frac{ - k}{ - 2.8} = 0.429 \\ - k = ( - 2.8)(0.429) = - 1.20 \\ k = 1.20[/tex]
