# 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

- SqdancefanLv 74 years agoFavourite 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.

- DrakeLv 54 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.