Which of the following is not a linear equation?

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5+4x= y−3

x+2y = y−x

3−x=

y^{2}

x+y= 0

answer is C.

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Detailed Solution

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.
1).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.
2).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
⇒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.
3).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.
4) x+y=0.
It can be written as