Question

How do you solve for $y$ in $6x + 3y = 9$?

Answer 1

Hint: In this question, we have been asked to find the value of $y$ in the given equation. But we cannot find the exact value of $y$. So, shift all the terms to the other side such that only $y$ remains on one side. This is the general value of $y$ and this is our answer.

Complete step by step answer:
We are given an equation in terms of $y$ and $x$, and we have been asked to find the value of $y$. Since the given equation is a linear equation in two variables, we want two equations in order to be able to find the value of the variables - $y$ and $x$.
Now, since we have only one equation, we cannot find the exact value of $y$. Hence, we will find the general value of $y$. Let us see how it is done.
$ \Rightarrow 6x + 3y = 9$ …. (given)
Shifting the term containing $x$ to the other side, we get,
$ \Rightarrow 3y = 9 - 6x$
Dividing the entire equation by the variable of $y$,
$ \Rightarrow y = \dfrac{{9 - 6x}}{3}$
On simplifying, we get,
$ \Rightarrow y = 3 - 2x$
Hence, this is the general value of $y$. On putting any value in $x$, we will find the value of $y$.

Note: What is a linear equation?
A linear equation is an equation whose degree is $1$. It means that no matter how many terms are there in an equation, the degree of all the terms should be equal to or less than $1$.
For example: The equation $a{x^2} + bx + c = 0$ is not a linear equation as the degree of this equation is $2$. It means that one of the terms of this equation has a degree greater than $2$. Such equations are called quadratic equations.