Answer:
To determine whether a linear inequality is in two variables, you need to check if it has the following characteristics:
Variables: A linear inequality in two variables will have two variables, typically represented as
�
x and
�
y. These variables are usually raised to the first power (not squared or cubed, etc.).
Linear Terms: The terms in the inequality should be linear, which means that the variables are not multiplied or divided by each other. They can be multiplied by constants (coefficients), added, subtracted, or standalone variables, but they should not be involved in more complex operations like squaring, square roots, etc.
Inequality Symbols: The inequality should contain symbols such as
<
< (less than),
≤
≤ (less than or equal to),
>
> (greater than), or
≥
≥ (greater than or equal to) to denote the relationship between the expressions on either side of the inequality.
Coefficients: Linear inequalities may contain coefficients, which are constants multiplied to the variables. These coefficients can be any real numbers.
Here are a few examples to illustrate linear inequalities in two variables:
Linear Inequality 1:
2
�
−
3
�
≤
5
2x−3y≤5
Two variables:
�
x and
�
y
Linear terms:
2
�
2x,
−
3
�
−3y,
5
5
Inequality symbol:
≤
≤
Linear Inequality 2:
4
�
+
2
�
>
10
4x+2y>10
Two variables:
�
x and
�
y
Linear terms:
4
�
4x,
2
�
2y,
10
10
Inequality symbol:
>
>
Linear Inequality 3:
3
�
−
2
�
=
6
3x−2y=6
Two variables:
�
x and
�
y
Linear terms:
3
�
3x,
−
2
�
−2y,
6
6
Inequality symbol:
=
= (This one is not a linear inequality; it's a linear equation, as it contains an equal sign instead of an inequality symbol.)
In summary, a linear inequality in two variables contains two variables, linear terms (without complex operations like squaring or square roots), an inequality symbol, and possibly coefficients. If these characteristics are present, you can determine that the inequality is in two variables.
Explanation: