Question

How do you solve for ‘y’? $16x+9=9y-2x$.

Answer 1

Hint: Try to separate both the variables. Keep ‘x’ on one side and ‘y’ on the other side of the equation. Then convert the equation in terms of ‘y’ and do the necessary calculation to get the value of ‘y’.

Complete step-by-step solution:
The equation we have is $16x+9=9y-2x$.
Solving for ‘y’ means we have to convert the equation in terms of ‘y’ and get the value of ‘y’.
Keeping ‘x’ on one side and ‘y’ on the other side of the equation, we get
$\begin{align}
  & \Rightarrow 16x+2x+9=9y \\
 & \Rightarrow 18x+9=9y \\
\end{align}$
Since we have to get the whole equation in terms of ‘y’ so it can be written as
$\Rightarrow 9y=18x+9$
Dividing by ‘9’ on both the sides to reduce the coefficient of ‘y’, we get
 $\begin{align}
  & \Rightarrow \dfrac{9y}{9}=\dfrac{18x+9}{9} \\
 & \Rightarrow y=\dfrac{18x+9}{9} \\
\end{align}$
Taking common ‘9’ from the numerator on the right hand side of the equation, we get
$\Rightarrow y=\dfrac{9\left( 2x+1 \right)}{9}$
Cancelling out ‘9’ both from numerator and denominator, we get
$y=2x+1$
This is the required solution.

Note: Since there are two variables and only one equation, we are getting ‘y’ in terms of ‘x’ while solving for ‘y’. The same is applicable if we would solve for ‘x’. So we need at least one more equation to get the value of ‘y’ which will be independent of ‘x’. hence for the equation given in the question, we are getting ‘y’ in terms of ‘x’ as there is only one equation with two different variables.