Determine whether the system of equations has one solution, no solution, or infinitely many solutions: 2x + 3y = 6 and 4x + 6y = 12


  1. Step-by-step explanation:
    we have
    2x + 3y = 6
    4x + 6y = 12
    do you see it right away ? both equations describe the same function or line.
    the second equation is just the first equation with everything multiplied by 2. but because that happened on both sides of the equation, the equation itself is not changed.
    we could divide equation 2 by 2 again, or multiply it further by e.g. 15 (as always on both sides of the equation) or, or, or …
    it would not change the information defined by the equation, and the corresponding line would still be the same.
    so, both equations represent the same line.
    that means both lines are covering each other perfectly (as they are identical), and so we have infinitely many intersections or solutions.


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