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To determine if the given equation [tex]\( y = 6 \)[/tex] is a linear equation in two variables, we begin by understanding what constitutes a linear equation in two variables.
A linear equation in two variables can generally be written in the form:
[tex]\[ Ax + By = C \][/tex]
where [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex] are constants, and [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are the variables.
Let's examine the given equation:
[tex]\[ y = 6 \][/tex]
This equation defines a straight line where the value of [tex]\( y \)[/tex] is always 6, regardless of the value of [tex]\( x \)[/tex]. To put this into the standard form, [tex]\( Ax + By = C \)[/tex], we can rewrite the equation as:
[tex]\[ 0x + 1y = 6 \][/tex]
Here, [tex]\( A = 0 \)[/tex], [tex]\( B = 1 \)[/tex], and [tex]\( C = 6 \)[/tex].
- The term [tex]\( 0x \)[/tex] signifies that there is no [tex]\( x \)[/tex] component present in this equation.
- The term [tex]\( 1y \)[/tex] indicates the presence of the [tex]\( y \)[/tex] component.
- The constant term [tex]\( C \)[/tex] is 6.
Since the equation [tex]\( 0x + 1y = 6 \)[/tex] still fits the general form of a linear equation in two variables, it is considered a linear equation, despite the absence of the [tex]\( x \)[/tex] variable.
Thus, we conclude that the given equation [tex]\( y = 6 \)[/tex] is indeed a linear equation in two variables. Therefore, the answer is:
[tex]\[ \boxed{\text{True}} \][/tex]
A linear equation in two variables can generally be written in the form:
[tex]\[ Ax + By = C \][/tex]
where [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex] are constants, and [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are the variables.
Let's examine the given equation:
[tex]\[ y = 6 \][/tex]
This equation defines a straight line where the value of [tex]\( y \)[/tex] is always 6, regardless of the value of [tex]\( x \)[/tex]. To put this into the standard form, [tex]\( Ax + By = C \)[/tex], we can rewrite the equation as:
[tex]\[ 0x + 1y = 6 \][/tex]
Here, [tex]\( A = 0 \)[/tex], [tex]\( B = 1 \)[/tex], and [tex]\( C = 6 \)[/tex].
- The term [tex]\( 0x \)[/tex] signifies that there is no [tex]\( x \)[/tex] component present in this equation.
- The term [tex]\( 1y \)[/tex] indicates the presence of the [tex]\( y \)[/tex] component.
- The constant term [tex]\( C \)[/tex] is 6.
Since the equation [tex]\( 0x + 1y = 6 \)[/tex] still fits the general form of a linear equation in two variables, it is considered a linear equation, despite the absence of the [tex]\( x \)[/tex] variable.
Thus, we conclude that the given equation [tex]\( y = 6 \)[/tex] is indeed a linear equation in two variables. Therefore, the answer is:
[tex]\[ \boxed{\text{True}} \][/tex]
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