# 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?

Relevance

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.

• 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.