Question

Which of the following is not a linear equation?
A. x + y = 6
B. x2 – 5x + 6 = 0
C. y = 2x
D. x = 0

Answer 1

Hint: The standard form of linear equation in two variables is ax + by + c = 0. Linear equation in one variable is ax + b = 0 or ay +b = 0. Now, compare the options given in the equation with the standard forms of linear equations.

Complete step by step answer:
A linear equation in two variables is an equation which is written in the form of ax + by + c = 0 where a, b and c can be any real number.
A linear equation in one variable is written as: ax + b = 0 or ay + b = 0 where a, b can be any real number.
Now, by keeping in mind the above definition of linear equation in different number of variables check whether the options given in question are linear or not :
a). x + y = 6
Rewriting the above equation as x + y – 6 = 0. You can see that this equation is in the form of a linear equation in two variables ax + by + c = 0 where a =1, b = 1 and c = -6. Hence, this option is a linear equation.
b). x2 + 5x – 6 = 0
The above equation cannot be written in any form of linear equation (ax + by + c =0, ax + b =0 or ay + b = 0) that we have described above so the above equation is not a linear equation.
c). y = 2x
Rewriting the above equation as 2x – y = 0 which you can see is in the form of ax + by + c = 0 where a = 2, b = -1 and c = 0 so the above equation is a linear equation.
d). x = 0
The above equation is in the form of ax + by + c = 0 where a =1, b = 0 and c = 0. Hence, the above equation is a linear equation.
From the above, we have concluded that option (b) is not a linear equation.
Hence, the correct option is (b).

Note: There is an alternative way of solving the above problem: a linear polynomial is the polynomial whose degree is 1 so a linear equation also has the degree 1 so the equation whose degree is not 1 is not a linear equation. As you can see only the option (b) is having a degree 2 (which is not equal to 1) so option (b) is not a linear equation.