We have defined the equation with two unknowns \[\blue p \cdot {x} + \green q \cdot {y} +\purple r=0\] Please note that linear equations with two unknowns of the form \[\blue{p_1} \cdot {x} + \green{q_1} \cdot {y} +\purple {r_1}=\blue{p_2} \cdot {x} +\green{q_2} \cdot {y} + \purple{r_2}\] can be rewritten to the above form by subtracting #\blue{p_2} \cdot {x}#, #\green{q_2} \cdot {y}# and #\purple {r_2}# from both sides of the equation.

Example

\[\begin{array}{rcl} \blue 3 \cdot {x}+\green{5} \cdot {y}+\purple 6&=& \green{-4} \cdot {y}+\purple{5}-\blue{2} \cdot {x} \\
\\
\blue 5\cdot x+\green 9 \cdot y + \purple 1&=&0
\end{array}\]