Question

Which of the following is not a linear equation?
\[\begin{align}
  & A.5+4x=y-3 \\
 & B.x+2y=y-x \\
 & C.3-x={{y}^{2}}+4 \\
 & D.x+y=0 \\
\end{align}\]

Answer 1

Hint: For this question, we will first understand the definition of linear equations. After that, we will pick our options and check from the definition if they are linear equations or not. Using this, we will find the equation which is not linear.

Complete step by step answer:
Let us first understand what linear equations are.
The equations which have the maximum degree of variable as 1, are called linear equations. For example: x+y = 2. In this equation, we have two variables x and y. Both variables have degree 1 (exponent power). So it is a linear equation.
Now let us look at our given option.
 $ A.5+4x=y-3 $ .
In this equation, we have two variables x and y. Equation can be written as $ 5+4{{x}^{1}}={{y}^{1}}-3 $ .
As we can see both variables have power as 1 i.e. both have degrees as 1. So this equation is a linear equation.
 $ B.x+2y=y-x $ .
Let us first simplify our equation by taking x and y to one side, we get, $ x+2y-y+x=0\Rightarrow 2x+y=0 $ .
It can be written as $ 2{{x}^{1}}+{{y}^{1}}=0 $ .
Here both variables x and y have degree 1 so this equation is a linear equation.
 $ C.3-x={{y}^{2}}+4 $ .
In this equation, we have two variables x and y. As we can see variable y has the power of 2 which means it is of degree 2. Hence, the equation has a degree higher than 1. So this equation is not a linear equation.
 $ D.x+y=0 $ .
It can be written as $ {{x}^{1}}+{{y}^{1}}=0 $ .
Since both variables, x and y have degree 1 so this equation is a linear equation.
Hence option C is the correct answer.

Note:
 Students should try to solve for variables before finding the degree. Equations having degree 2 are called quadratic equations. Option C is a quadratic equation. Note that any equation can have any number of variables but all variables should have degree 1 so that equation is linear.