Two equations with two unknowns

In most equations there is one unknown, but what happens if there are two?

 

$$ \large x = y + 4 $$

 

Here there are infinitely many solutions for \( \large x \) and \( \large y \). Every time \( \large x \) is 4 greater than \( \large y \), the equation is true.

 

\( \large x = 5, \; y = 1 \)

\( \large x = 6, \; y = 2 \)

\( \large x = 10, \; y = 6 \)

 

All these solutions are correct, and the sequence continues infinitely.

 

If we add another equation, we get a system of equations with two unknowns:

 

$$ \large x = y + 4 $$

$$ \large y = 8 - x $$

 

Now we have two equations with two unknowns, and in most cases it is possible to find a specific solution where both equations are satisfied simultaneously.