Question

How do you solve for y in the equation \[2x + y = 6\] ?

Answer 1

Hint: Given the equation is having two variables \[x\] and \[y\] . We have to solve the equation for \[y\] that is converting this in the form \[y = \] . Then for different values of \[x\] we will get different values of \[y\] . So simply shift all the terms other than \[y\] on the other side of the \[ = \] sign. Then we will get the equation for \[y\] .

Complete step-by-step answer:
Given that,
  \[2x + y = 6\]
This is an equation with degree 1 but two variables. So let’s rearrange the terms to get this in the form of \[y\] .
Shift the term \[2x\] on the other side of the equation.
  \[ \Rightarrow y = 6 - 2x\]
Now if we observe that there is only \[y\] on the LHS of the equation. This is our answer.
If we simplified it further we can take 2 common terms from the terms on RHS.
  \[ \Rightarrow y = 2\left( {3 - x} \right)\]
Now just putting the values of x we can get the values of \[y\] .
So, the correct answer is “ $ y = 2\left( {3 - x} \right) $ ”.

Note: Note that we are asked to find the equation in the form of \[y\] . If we were asked to find in the form of \[x\] then we have to shift the term with \[y\] on the other side.
  \[ \Rightarrow x = \dfrac{{6 - y}}{2}\]
Also note that when any number or term shifts from one side of the equation to the other side then its sign changes. That is if it is positive on one side of the equation then it becomes negative on the other side and vice versa.