Question

How do you solve for y in \[ry + s = tx - m\] ?

Answer 1

Hint: Here in this question, we have to solve the given equation to the y variable. The given equation is the algebraic equation with two variable x and y this can be solve by add or subtract the necessary term from each side of the equation to isolate the term with the variable y, then multiply or divide each side of the equation by the appropriate value, while keeping the equation balanced then solve the resultant balance equation for the y value.

Complete step by step answer:
In mathematics we have an algebraic equation where the algebraic equation is a combination of variables and constant. Consider the given equation
\[ry + s = tx - m\]--------(1)
Where x and y are the variables
r, s, t and are the constant terms
Now, we have to solve the above equation for the variable y
Subtract s on both side of equation (1), then
\[ry + s - s = tx - m - s\]
On simplification, we get
\[ry = tx - m - s\]
We want to solve the equation for y, then we have to move r to the RHS side, by dividing both side of equation by r, then
\[\dfrac{r}{r}y = \dfrac{{tx - m - s}}{r}\]
Again, by simplification, we get
\[y = \dfrac{{tx - m - s}}{r}\]
Or it can be written as
\[ \therefore y = \dfrac{1}{r}\left( {tx - m - s} \right)\]

Hence, the required solution is \[y = \dfrac{{tx - m - s}}{r}\].

Note: In this question we solve the given equation for the one variable. While shifting the terms we must take care of signs. When the term is moving from one side to another side the sign will change. We have another parameter to term which we want to determine we divide the parameter. On simplifying the terms and we obtain the solution for the question.