Question 689901
{{{x = 4y + 1}}} and 

{{{x = 4y – 1}}}

if you assign a number to {{{x}}} and solve both equation for {{{ y}}} you will need to get same value for {{{ y}}} IF they have same solution

let's check it:

let's {{{x=0}}}

 {{{0 = 4y + 1}}} ...solve for {{{y}}}

{{{-1 = 4y }}}

{{{highlight(-1/4 = y) }}}

and

{{{0 = 4y – 1}}}

{{{1 = 4y}}}

{{{highlight(1/4 = y)}}}

since {{{highlight-1/4<>1/4  }}}, the two equations do {{{not}}} have the same solution; it means these lines are parallel and do not intersect 

check it on a graph

{{{ graph( 600, 600, -10, 10, -10, 10, 4y + 1, 4y -1) }}}


you also can come to same conclusion this way:

first write both of them in {{{slope-intercept}}} form {{{y=mx+b}}} like this:

{{{x = 4y + 1}}}..=>..{{{x-1 = 4y}}}.=>..{{{(1/4)x-1/4 =y}}}. or {{{y=(1/4)x-1/4 }}}

and

{{{x = 4y -1}}}..=>..{{{x+1 = 4y}}}.=>..{{{(1/4)x+1/4 =y}}}. or {{{y=(1/4)x+1/4 }}}

as you can see both lines have same slope {{{m=1/4}}} and, by definition, the lines with same slope are {{{parallel}}}

if the lines {{{parallel}}}, they have no intersection point, and they have no same solution