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2x-3y=6 and 3y-2x= -6

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Is this a system of equations you are supposed to solve? Because the solution to that would be "any x and y where y = -2 + (2/3)x". These two equations are essentially the same thing, as you can get one from the other by multiplying both sides by (-1).

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To show more detail from what Kate is saying, I will "solve" this system using elimination method

 2x - 3y = 6

-2x + 3y = -6

0x + 0y = 0

0 = 0

Since neither variable remains, we cannot solve for a variable.  Since the statement is true (0 does equal 0), we know that the equations are two forms of the same line

There is an infinite number of solutions.