Question

How do you write $x = 4y - 5$ in standard form and what is $A,B,C$?

Answer 1

Hint: First step is to move the variable terms on one side by performing the same mathematical operations on both sides of the equation. Next step is to move the constant terms on the same side by performing the same mathematical operations on both sides of the equation. Then, we will get the standard form of the given equation. Next, we have to compare the standard form of given equation with the standard form of linear equations in two variables and to determine the values of $A,B,C$.
$Ax + By = C$ is called the standard form of linear equations in two variables.

Complete step by step solution:
Given equation is $x = 4y - 5$.
We have to write $x = 4y - 5$ in standard form and find the value of $A,B,C$.
First step is to move the variable terms on one side by performing the same mathematical operations on both sides of the equation.
So, subtracting $4y$ from both sides of the equation.
$ \Rightarrow x - 4y = - 5$
Thus, $x - 4y = -5$ is the standard form of a given equation.
Next, we have to compare the standard form of given equation with the standard form of linear equations in two variables and to determine the values of $A,B,C$.
On comparing $x - 4y = -5 $ with $Ax + By = C$, we get
$A = 1$, $B = - 4$ and $C = -5$

Therefore, $x - 4y = -5$ is the standard form of the given equation and $A = 1$, $B = - 4$ and $C = -5$.

Note: 1. An equation which can be put in the form $Ax + By = C$, where $A$, $B$ and $C$ are real numbers ( $A$ and $B$ together cannot be zero) and $x,y$ are variables, is called linear equation in two variables. In the equation $Ax + By = C$, the value of $x$ and $y$ are always real.
2. It is customary to denote the variables in such equations by $x$ and $y$, but other letters may also be used.