Solving a System of 2 Equations

How do you solve this system of equations?
2x + 3y = 1
4x + 6y = 2
For some reason when I use the elimination method I get x and y to equal 0.
Is this correct and does this mean it has infinitely many solutions?

2x + 3y = 1---->- 4x - 6y = -2  {multiplied top equation by -2}
4x + 6y = 2------>4x + 6y = 2

when the new equations are added together you get:
0 = 0
if the variables disappear and you get a statement that is always true,
there are infinite solutions  {meaning these two equations represent the same line}

Additional Note:
if the variables disappear and you get a statement that is never true, then there is no solution
{meaning the lines would not cross or they are parallel lines}

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