Two-Step Equations 3

Directions: Using the digits 1 to 9, at most one time each, fill in the boxes to find the largest (or smallest) possible values for the sum of x and y.

Hint

Where do you want to put the largest numbers? Where should you put the 1 and the 2?

Answer

The largest value is 19 which can be achieved by the following:
1x-8=9 and 2y+3=7

The smallest value is -6.125 which can be achieved by the following:
8x-3=4 and 1y+9=2

Source: Erick Lee

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9 comments

  1. Just a note that the second equation with the y value should have a subtraction sign vice an addition sign in order for the solution to be correct. (__y – __ = __)

  2. I believe the answer should be as follows (this combines the results from TWO-STEP EQUATIONS 1 and TWO-STEP EQUATIONS 2):

    The largest possible sum is 24, achieved with the following equations:
    1x – 9 = 8 or 1x – 8 = 0 –> x = 17
    1y – 2 = 9 –> y = 7

    The least possible sum is -6 2/3, achieved with the following equations:
    9x – 1 = 2 or 9x – 2 =1 –> x = 1/3
    1y + 9 =2 –> y = -7

    • Woops! I take that back. In the attempt that I cited as an answer, I ignored that I can’t repeat numbers that I’ve used already. That adds to the complexity!

      My brain just grew. =)

  3. I think finding the smallest positive value would add to this problem.

    9x – 1 =2 and 8x +3 = 4 11/24 or .46

  4. 1x – 5 = 4
    x = 9
    2y + 2 = 8
    9 + 3 = 15
    I can only use numbers 1-9 once and i cant use negative numbers right( 1-9 it doesn’t say negative).

  5. 7x – 6 = 8
    x = 2

    4y + 5 = 9
    y = 1

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