Question

Determine the value of k so that the lines kx-y=-1/3 and 3y=1-6x will not intersect?

Answer 1

\[kx-y=-\frac{ 1 }{ 3 }................(1)\]\[6x+3y=1.....................(2)\]
can u find out slopes for those two lines?

Answer 2

ok use the standard form
\[y=mx+c, ~~where~~m=slope.of.the.line\]
so for the first equation
\[y=kx+(1/3)\]so for this equation slope
\[m_1=k\]and for second equation we can write
\[3y=1-6x \\y=(1/3)-2x\\y=-2x+(1/3)\]
so for this equation slope will be
\[m_2=-2\]
now,they will never intersect if their slopes are equal so--\[m_1=m_2\\k=-2\]
so for k=-2 they will never intersect

Answer 3

got this? @jelolopera

Answer 4

this k= -2 will not intersect

Answer 5

you can check your answer is correct or not by putting k=-2 in the first equation then it will become
\[-2x-y=-1/3\\6x+3y=1\]and the second equation is also
\[6x+3y=1\]
so basilcally the two equations are same means they are parallel so they will never intersect

Answer 6

yeah :)