Question

Identify which of the following is not a linear equation in two variable?

• A. $2^{2}x+7=y^2$
• B. $x+3y=z$
• C. $\frac{7y}{x}+3=\frac{1}{x}$
• D. $x^3-y^3=3^3$

Answer 1

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

$x^3-y^3=3^3$

For a equation to be linear in two variable, exponent of both variable should be $1$ i.e. and that equation will represent straight line.

$\underset{–}{option\left(a\right)}:$ $2^{2}x+7=y^2$
This equation have two variables but is not linear because variable $y$ has exponent $2$. So, this is not linear equation in two variable.

$\underset{–}{option\left(b\right)}:$ $x+3y=z$
This is linear equation but have three variable $x,y$ and $z$.
So,this is not linear equation in two variable.

$\underset{–}{option\left(c\right)}:$ $\frac{7y}{x}+3=\frac{1}{x}$
On simplifying by transposing $3$ to RHS and $\frac{1}{x}$ to LHS we get,
$\frac{7y}{x}-\frac{1}{x}=-3\Rightarrow \frac{7y-1}{x}=-3\Rightarrow 7y-1=-3x\Rightarrow 7y+3x=1$

This is linear equation in two variable.

$\underset{–}{option\left(d\right)}:$ $x^3-y^3=3^3$
This is not linear equation because both variable have $3$ as their exponent.