Question

How many solutions does the following equation have?
$6(y-8)=6y-48$

Answer 1

Detailed step-by-step solution:
Let’s solve the equation to find the solution. To do this, we will simplify the given equation as much as possible. The given equation is:
$6(y-8)=6y-48$
$6y-48=6y-48$ (using distributive property)
$6y-48+48=6y-48+48$ (adding $48$ to both sides)
$6y=6y$
$6y-6y=0$ (moving all the like terms to the left side)
$0=0$ (the L.H.S. is reduced to $0)$
The original equation was simplified and we were left without the variable $“y”$ in it. We were not able to solve the equation to obtain a unique value of $“y”.$ But this also means that the original equation will always be satisfied with any value of $“y”.$
Example: Let $“y”=0$
$6\left(0\right)-48=6\left(0\right)-48$
$-48=-48$
Let $“y”=1$
$6\left(1\right)-48=6\left(1\right)-48$
$-42=-42$
Hence, equations, $L.H.S.=R.H.S.$
This will continue for each value of $y.$
Therefore, it has infinitely many solutions.
$\Rightarrow$ Infinitely many solutions: The linear equation in one variable has infinitely many solutions when each side is simplified to obtain an equation expressed in the form of $ax+b=ax+b,$ where $a$ and $b$ are two integers, and $x$ is a variable. An equation has infinitely many solutions if every value of the variable makes the equation true.

So, option A is the correct answer.