algebra

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if 5 times the first number plus 3 times the second number equals 47 and 10 times the first number minus 4 times the second number equals 54, what are the numbers?
please explain the steps

  • algebra -

    5x + 3y = 47
    10x - 4y = 54

    substitution:
    5x = 47 - 3y, so 10x = 94-6y, thus

    10x-4y = 94-6y - 4y = 54
    -10y = -40
    y=4
    so, x = 7

    elimination:
    multiply the first equation by 4 and the 2nd by 3

    20x+12y = 188
    30x-12y = 162
    add them, and the y's go away:
    50x = 350
    x=7
    so, y=4

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