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5 May, 15:36

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution.

-20x + 30y = - 3

8x - 12y = - 3

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  1. 5 May, 15:53
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    No solution.

    Step-by-step explanation:

    A system has only one solution if it ends at ax = b, in which a is different than 0.

    If it ends at 0x = 0, the system has infinitely many solutions.

    If it ends at a division by 0, or 0 = constant (different than 0), the system is inconsistent.

    Our system is:

    -20x + 30y = - 3

    8x - 12y = - 3

    I am going to multiply the top equations by 2 and the bottom equation by 5, and add them. So

    -40x + 60y = - 6

    40x - 60y = - 15

    So

    -40x + 40x + 60y - 60y = - 6 - 15

    0x + 0y = - 21

    We cannot divide 21 by 0, which means that this system of equations has no solution.
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