Question

Which of the following is/are not linear equation(s)?

• A. $3x+5y-7z=2x^2$
• B. $5y-7zx=29x+30$
• C. $\frac{3x+7y}{9z+7x}=2$
• D. $x-2x^2+3x^3=4$

Answer 1

Answer: (A), (B), (D)

The correct options are
A $3x+5y-7z=2x^2$
B $5y-7zx=29x+30$
D $x-2x^2+3x^3=4$

An equation is said to be a linear equation if the degree of that equation is one.

The equations, $3x+5y-7z=2x^2$ and $5y-7zx=29x+30$ are not linear equations as their degree is two.

The equation, $\frac{3x+7y}{9z+7x}=2$ is a linear equation as it can be reduced to the linear form. This is shown below:
$\frac{3x+7y}{9z+7x}=2$
Multiply both sides by $9z+7x$,
$\frac{3x+7y}{9z+7x}\times (9z+7x)=2\times (9z+7x)$
$⟹3x+7y=18z+14x$
$11x-7y+18z=0$

The equation, $x-2x^2+3x^3=4$ is also not a linear equation as its degree is three.