Question

How do you solve for w in the equation \[5w+9z=2z+3w\]?

Answer 1

Hint: Rearrange the terms of the given equation by taking the terms containing the variable ‘w’ in the L.H.S. and taking the other terms to the R.H.S. Now, apply simple arithmetic operations like: - addition, subtraction, multiplication, and division, whichever needed, to simplify the equation. Find the value of ‘w’ in terms of ‘z’ to get the answer.

Complete step by step answer:
Here, we have been provided with the equation: - \[5w+9z=2z+3w\], and we are asked to solve this equation for the value of w. That means we have to find the value of ‘w’ in terms of ‘z’.
As we can see that the given equation is a linear equation in two variables ‘w’ and ‘z’, so we can only find the value of one of the variables in terms of the other. So, now taking the terms containing the variable ‘w’ in the L.H.S. and taking all other terms to the R.H.S., we get,
\[\begin{align}
  & \Rightarrow 5w-3w=2z-9z \\
 & \Rightarrow 2w=-\left( 9z-2z \right) \\
 & \Rightarrow 2w=-7z \\
\end{align}\]
Dividing both the sides with 2, we get,
\[\Rightarrow \dfrac{2w}{2}=\dfrac{-7z}{2}\]
Cancelling the common factor in the L.H.S, we get,
\[\Rightarrow w=\dfrac{-7z}{2}\]
Hence, the value of w is \[\dfrac{-7z}{2}\].

Note:
One may note that we haven’t found any numerical value of w. This is because there were two variables and only one equation. To find the numerical value we will need one more relation between ‘w’ and ‘z’. In general, remember that to solve the system of equations containing ‘n’ variables we need ‘n’ number of relations between these variables. If it is not present then we can only find the value of one variable in terms of the other.