Question

How do you solve for y: $\dfrac{{zy}}{x} = b$?

Answer 1

Hint: We will first of all, multiply both the sides of the equation by x, then we will just divide the sides of the equation thus obtained by z to get the value of y.

Complete step by step solution:
We are given that we are required to solve for y, the given equation $\dfrac{{zy}}{x} = b$.
Let us, first of all multiply both the sides of the given equation by x, we will then obtain the following equation with us:-
$ \Rightarrow x \times \dfrac{{zy}}{x} = x \times b$
Simplifying the left hand side of the above equation by crossing – off the common x from numerator and denominator and simplifying the right hand side as well, we will then obtain the following equation with us:-
$ \Rightarrow zy = bx$
Let us now divide both the sides of the given equation by z, we will then obtain the following equation with us:-
$ \Rightarrow \dfrac{{zy}}{z} = \dfrac{{bx}}{z}$
Simplifying the left hand side of the above equation by crossing – off the common z from numerator and denominator, we will then obtain the following equation with us:-
$ \Rightarrow y = \dfrac{{bx}}{z}$

Thus, we have the required answer which is the value of y is $\dfrac{{bx}}{z}$.

Note:-
The students must note that when we crossed – off $x$ from both the numerator and denominator, we made a statement that x can never be equal to 0. The similar thing happened with z as well, when we crossed – off z from both the numerator and denominator in the left hand side. Because we can never cross – off any variable which can be equal to 0. We also cannot multiply the equation by any such variable as well. Here, since we are already given x in the denominator, therefore, it cannot be zero, otherwise it would not have been defined. Similarly, if z would have been zero, the whole equation would have become zero, which does not make any sense.