Question

The linear equation $x = 5$ in two variables can be written as:
1) $1.x + 5 = 10$
2) $0.x + 1.y + \left( { - 5} \right) = 0$
3) $1.x + 0.y + \left( { - 5} \right) = 0$
4) $1.x + 1.y + \left( { - 5} \right) = 0$

Answer 1

Hint: An equation is said to be linear in two variables if it is written in the form of$ax + by + c = 0$, where a, b & c are real numbers and coefficients of$x\& y$, where a and b respectively are not equal to zero. For example $10x + 4y = 3$ and $ - x + 5y = 2$ are linear equations in two variables.

Complete step-by-step answer:
Standard form of any linear equation in two variables is $ax + by + c = 0$
As given in the question $x = 5$
We have to convert the equation in the standard format
From the question
$
  x = 5 \\
   \Rightarrow x - 5 = 0 \\
 $
Now we convert the above equation in $ax + by + c = 0$format.
For this we can write this equation as:
$1.x + \left( { - 5} \right) = 0$
Multiplying by $1$ it does not affect the equation.
Because the $y$ term is not given in the equation so we can write it as:
$1.x + 0.y + \left( { - 5} \right) = 0$ …………….$\left( 1 \right)$
Here we can see that the value of $a = 1,b = 0\& c = \left( { - 5} \right)$
So from equation $1$ we can say that this is the perfect form of linear in two variables.
Hence option C is the correct answer.

Note: We have to remember that the linear in two variables if it is written in the form of$ax + by + c = 0$, where a, b & c are real numbers and coefficients of$x\& y$. In the problem, we convert the given value $x = 5$ in linear equation format. For this, we put the values of $x\& y$ in the equation. Hence we get the correct answer.