Question

How do you solve for y in $x+a=yb$ ?

Answer 1

Hint: In this problem, we are given an equation in which there are two variables x and y. On the left hand side of the equation is the variable x and on the right hand side of the equation is the variable y. So, we simply need to divide both sides of the equation by b and then we will get y in terms of x.

Complete step by step answer:
Algebra is that branch of mathematics that deals with the use of variables in the form of alphabets. Variables are mathematical quantities or amounts, the value of which is not known. Variables are also called unknowns as we are not aware of their values. In a certain problem, there may be one or more than one variable. There is an axiom regarding variables which says that in order to solve for all the variables of a problem, there must be that many numbers of distinct equations as the number of variables in the problem. If the number of distinct equations equals the number of variables, then we get a definite value for each variable. If that is not the case, then there will exist an infinite number of solutions for the variables.
In our given problem, the given equation is $x+a=yb$ . Here, we can see that the equation involves the use of two variables viz. x and y. But, to our knowledge, the number of equations are given to be one and we are not told of any other relation between x and y. This means that there exists an infinite number of solutions.
To solve for y, we express y in terms of x. This is done by,
$\begin{align}
  & \Rightarrow x+a=yb \\
 & \Rightarrow y=\dfrac{1}{b}\left( x+a \right) \\
\end{align}$

Therefore, we can conclude that we can solve for y as $y=\dfrac{1}{b}\left( x+a \right)$

Note: The problem involves one equation and two variables. This may seem at first to be unsolvable to us. But we must understand what the question demands and then solve for y in terms of x. We may not get a defined value for y, but that is not required.