Equations with Two Variables
Algebra · Grade 7
§1. Introduction — From One Variable to Two
You have already studied equations with one variable, such as:
In each of these, there is only one unknown (the variable x), and we find a single number (or a few numbers) that make the equation true.
Now we take a big step forward. What happens when an equation contains two different variables?
Each of these equations contains two unknowns — usually called x and y. To solve them, we need to find values for both variables at the same time.
§2. What Is an Equation with Two Variables?
Definition
An equation with two variables (уравнение с двумя переменными) is an equation that contains two different unknowns (usually denoted x and y). Both variables can take different values.
Such equations are more complex than one-variable equations because we must find pairs of numbers rather than single numbers.
One Variable
2x + 3 = 11
Solution: x = 4
A single number
Two Variables
2x + y = 11
Solution: (x; y) = (4; 3)
A pair of numbers