Solving of Equation with Two Variables
Consider equation with two variables `f(x,y)=0`.
Pair of values that makes from equation correct equality is called solution of the equation. If we are given equation with two variables x and y, then it is a rule to write its solution as (x;y) (x is on first place and y is on second).
So, pairs (10;0), (16;2), (-2;4) are solutions of equation `x-3y=10` (for example, (10;0) is solution because `10-3*0=10`), while (1;5) is not solution, because `1-3*5=-14!=10`.
This equation has other solutions. To find them it is convenient to express one variable in terms of another, for example x in terms of y, obraining equation `x=10+3y`. Choosing any value of y, we can calculate value of x. For example, if y=7 then `x=10+3*7=31`, therefore, pair (31;7) is solution of equation.
Equations with two variables are called equivalent if they have same solutions.
For equations with two variables all facts about equivalent transformations are true.