91Ó°ÊÓ

When solving linear equations, the first step is often to isolate the variable term. This means getting the term with the variable (\(y\) in our example) all by itself on one side of the equation. In the original exercise, our goal is to isolate \(-13y\).
To do this, we performed an operation on both sides of the equation. This usually involves either adding or subtracting the same number from both sides, which keeps the equation balanced because whatever you do to one side, you must do to the other.
Here, we subtracted 9 from both sides to remove the constant term on the same side as the variable. This left us with the equation: $$35 - 9 = -13y + 9 - 9$$, which simplifies to $$26 = -13y.$$
Now, the variable term \(-13y\) is isolated.

Handling constants on both sides of an equation is a crucial skill in algebra. Constants are numbers that do not contain variables. In our example, the constants are 35 and 9. When you have constants on both sides, your goal is to move them to one side to simplify the equation.
This often involves simple arithmetic. Remember, you can add or subtract the same value from both sides without changing the equation's essence.
In our case, after identifying the constant we wanted to isolate the variable (\9\ from the right-hand side), we performed the subtraction: $$35 - 9 = -13y + 9 - 9$$, which simplifies down to $$26 = -13y.$$ This manipulation positioned us closer to solving for the variable.

Once you have isolated the variable term, the next step is to solve for the variable itself. This frequently means performing the opposite action of what is currently being applied to the variable.
In our example, after isolating \(-13y\), we needed to solve for \y\. The term was being multiplied by \-13\, so the opposite operation is division.
To isolate \y\, we divided both sides of the equation by \-13\: $$\frac{26}{-13} = \frac{-13y}{-13}$$. By simplifying, we found $$y = -2$$.
Following these steps—isolating the variable term, dealing with constants, and solving for the variable—will guide you through many algebra problems!