Help with simple looking (but not!) problem?

Let's suppose I have two tables X and Y. Both tables contain two elements so X = (5,3) and Y = (4,1).

Now suppose I don't know the values of the elements. But I do know the results of their addition. So I can write four equations representing the addition of each combination of table elements:

x1 + y1 = 9

x1 + y2 = 6

x2 + y1 = 7

x2 + y2 = 4

Am I right in thinking, actually, I can't work out the table elements based on these equations other than by making a 'logical guess' at the value of one of them?

2 Answers

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  • 4 years ago
    Favourite answer

    You have four equations in four unknowns. Unfortunately, the system of equations is dependent, so has an infinite number of solutions.

    .. x1 = 6 - y2

    .. x2 = 4 - y2

    .. y1 = 3 + y2

    .. y2 = anything you like.

  • Drake
    Lv 5
    4 years ago

    x₁ + y₁ = 9

    x₁ + y₂ = 6

    x₂ + y₁ = 7

    x₂ + y₂ = 4

    y₁ = 9 - x₁

    x₂ + (9 - x₁) = 7

    x₂ = x₁ - 2

    (x₁ - 2) + y₂ = 4

    y₂ = -x₁ + 6

    x₁ + (-x₁ + 6) = 6

    0 = 0

    There is no certain solution that I could find! Could not obtain a certain value of anything.

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