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Question 970366: Which best describes the relationship between the lines with the equations -6x+21y=21 and -2x+7y=7?
[A] parallel
[B] perpendicular
[C] neither parallel nor perpendicular
[D] same line
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website! Which best describes the relationship between the lines with the equations  and  ?
[A] parallel
[B] perpendicular
[C] neither parallel nor perpendicular
[D] same line
to find out, we need a slope;as you know, two lines
that have  slope are  ,and do not intercept, there is no solution
two lines that have slope negative reciprocal to each other are 
where the lines lie on top of each other, one equation can be rearranged to be the other equation precisely; this means when solving, you would get  and  , there are infinite solutions in this case (every point along the line would be a solution)
so, first write both equations in a slope-intercept form
 => a slope is  and y-intercept is 
and
=> a slope is and y-intercept is
So, both the lines have same slope and same y- intercept which means the lines coincide and there are innumerable solutions (means any  or  value will satisfy the system of equations). So there are an infinite number of solutions, and this system is  .
that all leads us to the conclusion that your answer is:[D] same line
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