Question

How do you solve $5x - 3y = 14\;{\text{for}}\;y?$

Answer 1

Hint: There are two variables in the given equation, in order to solve the equation for one of the two variables, consider the other variable to be constant and perform algebraic operations in the equation to remove the other variable from the left hand side and send it to right hand side and make the required variable a dependent variable which will depend on the values of the other variable.

Complete step by step solution:
In order to solve the given equation for the value of y, we will first simplify the equation in such a way that all the terms in the equation (including variables and constants) except the variable y (for which we have been asked to solve the equation) should be on the right hand side of the equation and only variable y should be at the left hand side as follows
$ \Rightarrow 5x - 3y = 14$
Subtracting $5x$ from both sides of the equation, in order to remove it from left hand side,
$
   \Rightarrow 5x - 3y - 5x = 14 - 5x \\
   \Rightarrow - 3y = 14 - 5x \\
 $
Multiplying both sides with $ - 1$ in order to make coefficient of y positive,
$
   \Rightarrow - 1 \times ( - 3y) = - 1 \times (14 - 5x) \\
   \Rightarrow 3y = - 14 + 5x \\
 $
Now, dividing both sides with $3$, in order to make coefficient equal to one,
$
   \Rightarrow \dfrac{{3y}}{3} = \dfrac{{5x - 14}}{3} \\
   \Rightarrow y = \dfrac{{5x - 14}}{3} \\
 $
So, $y = \dfrac{{5x - 14}}{3}$ is the required solution for y in the equation $5x - 3y = 14$

Note: In this type of question, in which the equation has multiple variables, do not panic how to solve them. Just solve for the variable which you have been asked to solve for, and consider all other variables to be constant. Simplify the equation such that only the required variable should present at the left hand side.