Question 934343
given:
Line 1
{{{x}}}|	{{{y}}}
{{{-6}}}|	{{{3}}}
{{{3}}}|	{{{6}}}

first find equation of a line passing through given points:

 *[invoke change_this_name10094 -6, 3, 3, 6]
 

Line 2
{{{x}}}|	{{{y}}}
{{{-3}}}|	{{{1}}}
{{{3}}}|	{{{3}}}
 
*[invoke change_this_name10094 -3, 1, 3, 3] 

see both lines on a graph:

{{{ graph( 600, 600, -10, 10, -10, 10, (0.333333333333333)x + 2, (0.333333333333333)x + 5) }}}

From the graph, we can see that the two lines are parallel and will never intersect. So there are no solutions and the system is inconsistent. 

 according to Euclidean geometry, if two lines are distinct but have the same slope they are said to be parallel and have {{{no}}} points in common.

so, your answer is A. {{{0}}}

It is also  good to know that, according to non-Euclidean geometry (so called projective geometry) any pair of lines {{{always}}}{{{ intersects}}} at some point, but parallel lines do not intersect in the real plane. The line at infinity is added to the real plane. This completes the plane, because now {{{parallel}}}{{{ lines}}} intersect at a point which lies on the line at {{{infinity}}}. Also, if any pair of lines intersects at a point on the line at infinity, then the pair of lines is parallel.

 but we will keep A.{{{0}}} as an answer to your question