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2 times a number added to another number is 25. 3 times the first number minus the other number is 2

2 times a number added to another number is 25. 3 times the first number minus the other number is 20.

Let the first number be x. Let the second number be y. We're given two equations:

  • 2x + y = 25
  • 3x - y = 20
    • Since we have matching opposite coefficients for y (1 and -1), we can add both equations together and eliminate a variable.
    (2 + 3)x + (1 - 1)y = 25 + 20

    Simplifying, we get:
    5x = 45

    Typing this equation into the search engine, we get:
    x = 9

    To find y, we plug in x = 9 into equation (1) or (2). Let's choose equation (1):
    2(9) + y = 25
    y + 18 = 25

    Typing this equation into our search engine, we get:
    y = 7

    So we have (x, y) = (9, 7)

    Let's check our work for equation (2) to make sure this system works:
    3(9) - 7 ? 20
    27 - 7 ? 20
    20 = 20 <-- Good, we match!

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