Question

How do we solve for $y$ in the equation $xy - d = m$ ?

Answer 1

To solve this question, first we will isolate $xy$ at one side and then again we will isolate $y$ by removing $x$ from $xy$ by dividing both sides by $x$ while keeping the equation balanced. That’s how we will get the value of $y$ .

Complete Step by step answer:
First, we will try to keep $xy$ isolate in Left Hand Side by adding $d$ to each side of the equation to isolate the $y$ term while keeping the equation balanced:
$\Rightarrow xy - d + d = m + d \\\ \Rightarrow xy - 0 = m + d \\\ \Rightarrow xy = m + d \\\$
Now, to isolate y at one side, we have to remove $x$ form L.HS by dividing both side by $x$ while keeping the equation balanced:
$\Rightarrow \dfrac{{xy}}{x} = \dfrac{{m + d}}{x} \\\ \Rightarrow y = \dfrac{{m + d}}{x} \\\$
or, $y = \dfrac{m}{x} + \dfrac{d}{x}$
Hence, the value of y is $(\dfrac{m}{x} + \dfrac{d}{x})$ .

Note: Substitute Values into an Equation and Solve for a Variable Sometimes an equation with multiple variables, as in multiple letters. Most of these variables will be known, so we can replace the variables in our equation with the numbers that we know they are equal to.