91Ó°ÊÓ

Combining like terms is a fundamental process when working with linear equations. This involves simplifying the equation by merging terms that are similar, which usually means they have the same variable to the same power. In the given exercise, the equation started as \(5y + 2y - 1 = 6y\). Here, both \(5y\) and \(2y\) are like terms because they contain the variable \(y\). By adding these two terms together, we simplify the expression to \(7y - 1 = 6y\).
This process helps reduce the complexity of the equation, making it easier to isolate the variable in the following steps. Always look for coefficients with the same variable as an initial step to streamline your work.

Isolating the variable is the next crucial step in solving linear equations. This involves rearranging the equation so that the variable you are solving for stands alone on one side of the equation, usually the left side. In our exercise, we began with the equation \(7y - 1 = 6y\).
In order to isolate \(y\), we first subtract \(6y\) from both sides. After performing this operation, the equation becomes \(7y - 6y - 1 = 0\), which simplifies to \(y - 1 = 0\). This manipulation leaves us with a simpler equation where the variable \(y\) is more prominently featured and almost isolated for the final step.
Always keep in mind that reversing operations, like addition and subtraction, is often necessary to achieve this simplified form.

Solving the equation is the final step where you find the value of the variable. Once like terms have been combined and the variable isolated, you're usually left with a straightforward equation to solve. In this exercise, after isolating \(y\), we were left with the equation \(y - 1 = 0\).
To solve for the variable \(y\), we simply perform the inverse operation of subtracting 1, which is to add 1 to both sides of the equation. This balances the equation and results in \(y = 1\).
By following these methodical steps, you ensure that all operations are balanced, leading you to a correct solution. Always review your work to confirm that the solution satisfies the original equation.