Question

How do you rewrite $5x - 7 = y$ in standard form?

Answer 1

Hint: In order to rewrite the given equation in the standard form, transpose term containing $y$ from RHS to LHS to make the right-hand side of the equation equal to zero. Now rearrange the terms and compare it with the standard form to obtain the standardized form of the equation.

Complete step by step answer:
We are given a linear equation in two variables $x\,and\,y$ as $5x - 7 = y$.
The standard form for linear equations in two variables is of the form $ax + by + c = 0$ where $a,b,c$ are the constants and $a,b \ne 0$.
To rewrite the given equation in the standard form ,we have to perform transposition of terms from right-hand side toward left-hand side as to make the RHS part of the equation equal to zero.
So , after transposing the term containing $y$ from RHS to LHS , we obtain our equation as
$
   \Rightarrow 5x - 7 = y \\
   \Rightarrow 5x - 7 - y = 0 \\
 $
Rearranging terms, we get
$ \Rightarrow 5x + \left( { - 1} \right)y + \left( { - 7} \right) = 0$
Comparing the above equation with the standard equation $ax + by + c = 0$,we get the values for variables as
$
  a = 5 \\
  b = - 1 \\
  c = - 7 \\
 $

Therefore, the given equation in the standard form is equal to $5x + \left( { - 1} \right)y + \left( { - 7} \right) = 0$

Additional information:
Linear Equation in two variables: A linear equation in two variables is a equation which can be represented in the form of $ax + by + c $where $x$ and $y$ are the unknown variables and $a,b, c$are the numbers known where $a,b \ne 0$.
The highest degree of the variables in the linear equation is of the order 1.

Note: 1. Since in this question there are no like terms but if there are like terms in any equation, first combine all the like terms and then rearrange term to obtain the standard form .
2. Like terms are terms which have the same variable and same exponent power. Coefficients of the likes terms may differ.
4. The equation in this question is linear in nature , as the highest degree of both the variables is 1.
5. Remember the property of transpose of terms that whenever any term is transposed from one side to another, the sign of the term gets reversed.
6.The aim of transposition of terms is always to bring like terms together and isolate the variable .