Question

Which of the following equations represent linear equations in two variables?

• A. $y=2$
• B. $2x^2-5y=1$
• C. $x-y=1$
• D. $xy=5$

Answer 1

The correct option is C $x-y=1$

Standard from of line in two variables: $ax+by=c$, where $x,y$ are variables and $a,b,c$ are constants and the $a$ and $b$ cannot be zero.
Now,
$\Rightarrow y=2$, it can be written as $0x+y=2$. But the cofficient of $x$ cannot be zero. So, it does not represent a line in two variables.

$\Rightarrow 2x^2-5y=1$, the power of $x$ is not unity. So, it does not represent a line.

$\Rightarrow x-y=1$, it has two variable $x,y$ and coefficients are not zero. So, it represents a line in two variables.

$\Rightarrow xy=5$, it has two variables but the variables are multiplied together. This equation does not represent linear equations.