Answer :
To determine which among the given equations is not a linear equation, let's analyze each option step by step.
### Let's look at each equation:
- Option A) \( x + y = 4 \)
This equation is linear because both \(x\) and \(y\) are raised to the power of 1 and it can be written in the form \(ax + by = c\), where \(a\), \(b\), and \(c\) are constants.
- Option B) \( 2x - y = 1 \)
This equation is also linear for the same reason. Both variables \(x\) and \(y\) are to the power of 1 and it fits the form \(ax + by = c\).
- Option C) \( x^3 = 2 \)
This equation is not linear. The variable \(x\) is raised to the power of 3, which makes it a cubic equation rather than a linear one.
- Option D) \( y = 4 \)
This equation is linear because it can be considered in the form \(y = mx + c\) with \(m = 0\) and \(c = 4\), which indeed fits the form \(ax + by = c\) where \(a=0\), \(b=1\), and \(c=4\).
### Conclusion:
From the analysis, we can see that the equation \( x^3 = 2 \) in option C is the one that is not a linear equation. It is a nonlinear equation due to the power of 3 on the variable \(x\).
Therefore, the correct answer is:
C) [tex]\( x^3 = 2 \)[/tex]
### Let's look at each equation:
- Option A) \( x + y = 4 \)
This equation is linear because both \(x\) and \(y\) are raised to the power of 1 and it can be written in the form \(ax + by = c\), where \(a\), \(b\), and \(c\) are constants.
- Option B) \( 2x - y = 1 \)
This equation is also linear for the same reason. Both variables \(x\) and \(y\) are to the power of 1 and it fits the form \(ax + by = c\).
- Option C) \( x^3 = 2 \)
This equation is not linear. The variable \(x\) is raised to the power of 3, which makes it a cubic equation rather than a linear one.
- Option D) \( y = 4 \)
This equation is linear because it can be considered in the form \(y = mx + c\) with \(m = 0\) and \(c = 4\), which indeed fits the form \(ax + by = c\) where \(a=0\), \(b=1\), and \(c=4\).
### Conclusion:
From the analysis, we can see that the equation \( x^3 = 2 \) in option C is the one that is not a linear equation. It is a nonlinear equation due to the power of 3 on the variable \(x\).
Therefore, the correct answer is:
C) [tex]\( x^3 = 2 \)[/tex]
