Get expert advice and community support on IDNLearn.com. Discover in-depth answers to your questions from our community of experienced professionals.
Sagot :
To determine which of the given equations is not a linear equation, we need to check if each equation can be written in the standard form of a linear equation. A linear equation involves variables (like \( x \) and \( y \)) raised only to the first power and does not include products of these variables or any non-linear functions like \(\sin(x)\) or \(\exp(y)\).
Let's examine each equation:
### Equation A: \(\frac{1}{2} x + 3 y = 2\)
Here, \(\frac{1}{2} x\) and \(3 y\) are both linear terms because each variable is raised to the power of 1. This is a standard form linear equation.
### Equation B: \(x^3 - 5 y^2 = 4\)
In this equation, \(x\) is raised to the power of 3 and \(y\) is raised to the power of 2. Both of these terms are non-linear because the variables \(x\) and \(y\) are not raised solely to the first power.
### Equation C: \(x = 2\)
This represents a vertical line, which is indeed a linear equation because it can be viewed as \(1 \cdot x + 0 \cdot y = 2\).
### Equation D: \(y = 4\)
Similarly, this represents a horizontal line, which is also a linear equation because it can be seen as \(0 \cdot x + 1 \cdot y = 4\).
From this analysis, we can clearly see that the equation which is not a linear equation is:
[tex]\[ B) x^3 - 5 y^2 = 4 \][/tex]
So, the answer is B.
Let's examine each equation:
### Equation A: \(\frac{1}{2} x + 3 y = 2\)
Here, \(\frac{1}{2} x\) and \(3 y\) are both linear terms because each variable is raised to the power of 1. This is a standard form linear equation.
### Equation B: \(x^3 - 5 y^2 = 4\)
In this equation, \(x\) is raised to the power of 3 and \(y\) is raised to the power of 2. Both of these terms are non-linear because the variables \(x\) and \(y\) are not raised solely to the first power.
### Equation C: \(x = 2\)
This represents a vertical line, which is indeed a linear equation because it can be viewed as \(1 \cdot x + 0 \cdot y = 2\).
### Equation D: \(y = 4\)
Similarly, this represents a horizontal line, which is also a linear equation because it can be seen as \(0 \cdot x + 1 \cdot y = 4\).
From this analysis, we can clearly see that the equation which is not a linear equation is:
[tex]\[ B) x^3 - 5 y^2 = 4 \][/tex]
So, the answer is B.
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Thank you for visiting IDNLearn.com. We’re here to provide clear and concise answers, so visit us again soon.