Question

How do you solve for $y$ in $x - 2y = 2$?

Answer 1

Hint: This problem deals with a linear equation in two variables. Whenever you see this type of question, our objective is to end up with something y = something. We have to do this in steps. First of all isolating all the terms that contain our target variable which is y here on one side of the equation and everything else on the other side.

Complete step-by-step solution:
Given a linear equation in $x$ and $y$, which is $x - 2y = 2$.
We are asked to find the expression of $y$.
First we have to isolate the terms with $y$ in them.
Consider the given linear equation, as given below:
$ \Rightarrow x - 2y = 2$
In order isolate the terms with $y$ in them, we have to subtract $x$ on both the sides of the above equation, as given below:
$ \Rightarrow \left( {x - 2y} \right) - x = \left( 2 \right) - x$
Here brackets are involved in order to show what is happening, they have no other purpose.
$ \Rightarrow - 2y = 2 - x$
Now to make the terms with $y$ positive, we have to multiply with -1 on both sides of the above equation, which is given below:
$ \Rightarrow - \left( { - 2y} \right) = - \left( {2 - x} \right)$
On multiplication with -1, the equation obtained is given below:
$ \Rightarrow 2y = x - 2$
Now divide the above equation by 2, which removes 2 from $2y$, which is given below:
\[ \Rightarrow \dfrac{{2y}}{2} = \dfrac{{x - 2}}{2}\]
Which is the same as multiplying the equation on both sides with $\dfrac{1}{2}$, as given below:
\[ \Rightarrow \dfrac{{2y}}{2} = \dfrac{x}{2} - \dfrac{2}{2}\]
\[ \Rightarrow y = \dfrac{x}{2} - 1\]

The expression for y, is given by \[y = \dfrac{x}{2} - 1\].

Note: Please note that an equation is said to be linear equation in two variables if it is written in the form of $ax + by + c = 0$, where $a,b$ and $c$ are real numbers and the coefficients of $x$ and $y$, i.e, $a$ and $b$ are not equal to zero. The numbers $a,b$ are called the coefficients of the equation $ax + by + c = 0$. The number $c$ is called the constant of the equation $ax + by + c = 0$.