Question

Which of the following represents a linear equation in two variables?

• A.
  where, x is a variable and a, b are real numbers
• B.
  where, a, b, c are real numbers and xy ≠ 0, and x, y are variables
• C. =
  where, a, b, c are real numbers and + ≠ 0
• D.
  where, a, b, c are the variables and x, y are real numbers

Answer 1

The correct option is B

where, a, b, c are real numbers and xy ≠ 0, and x, y are variables

The general form of a linear equation is: $ax+by+c=0$
where $a$, $b$, $c$ are real numbers and $a$, $b$ are both not zero.

The last condition can be stated mathematically as $a^2+b^2\ne 0$
The only linear equation is:
$x^{2}a+y^{2}b=c$
where $x$, $y$ are real numbers and $xy\ne 0$, and $a$, $b$ are variables and $c=0$. Rest of the equations do not satisfy the condition of a linear equation in two variables.