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The first step in solving linear equations often involves combining like terms. Like terms are terms that contain the same variable raised to the same power. For instance, \(-10y\) and \(-3y\) are like terms because they both contain the variable \(y\).Combining like terms simplifies the equation, making it easier to solve. In the equation \(-10y - 3y = -39\), you add the coefficients of the like terms together. Coefficients are the numerical parts in front of the variables. Here, the coefficients \(-10\) and \(-3\) combine to become \(-13\).Thus, \(-10y - 3y\) simplifies to \(-13y\). The equation then becomes:\(-13y = -39\)

Once the equation is simplified by combining like terms, the next step is isolating the variable. The goal is to get the variable on one side of the equation and everything else on the other side. This simplifies the equation into a form that is easy to solve.In the example equation \(-13y = -39\), the variable \(y\) is already on one side of the equation, but it's multiplied by \(-13\). To isolate \(-13y\), you need to get rid of this multiplication by dividing both sides of the equation by \(-13\). This operation gives the solution for \(y\).So, dividing both sides by \(-13\), we get:\(-13y / -13 = -39 / -13\), which simplifies to \(y = 3\).Now the equation is solved and the value of the variable \(y\) is found to be \(3\).

Coefficients are the numbers that multiply the variables in an equation. They are integral in both combining like terms and isolating the variables. Understanding coefficients is crucial for simplifying and solving equations effectively.In the equation \(-10y - 3y = -39\), the numbers \(-10\) and \(-3\) are the coefficients of the variable \(y\). When combining like terms, you add these coefficients together to simplify the equation, resulting in the coefficient \(-13\). This simplified form, \(-13y\), still includes a coefficient.When isolating the variable, the coefficient determines how you manipulate the equation. In this case, dividing by \(-13\) isolates \(y\), showing its value in a straightforward manner. Knowing how to handle coefficients helps in efficiently solving linear equations.