<PRE><B>Question 590619</B>
4x-3y=2                   
5x+3y=6                   
12x-9y=6                  
10x+6y=2


y = (4/3)x - 2/3
y = (-5/3)x + 2
y = (4/3)x - 2/3
y = -5/3)x + 1/3


2 of the lines have the same slope and the same y intercept so they are identical.  if you graph these equations, they will look like one line rather than 2.
2 of the lines have the same slope and different y intercept so they are parallel.
you have 1 set of identical lines and 1 set of parallel lines that will intersect in 2 separate points on a graph.
for there to be a common solution, all 4 lines would have had to intersect in one common point on the graph.
since there is not one common solution for all 4 equations, this system of equations has no solution.


a graph of the lines will show the 2 points of intersection.
{{{graph(600,600,-5,5,-5,5,(4/3)x-(2/3),-(5/3)x+2,(4/3)x-(2/3),-(5/3)x+(1/3))}}}

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