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When solving an equation, one of the first steps is often to isolate the variable. The aim is to get the variable on one side of the equation all by itself. This usually involves doing the opposite operation of what is currently being done to the variable.
To isolate the variable in the equation \(-4y = 0\), you need to remove the multiplication by \(-4\) that is currently paired with \(y\). Isolation can involve operations like addition, subtraction, multiplication, or division. For this equation, you use division as it directly opposes the multiplication with \(-4\).
Understanding this concept is essential because it allows you to simplify equations step by step. Once the variable is isolated, you know the value it must take for the equation to be true, thus solving it.

Division is a very powerful tool in algebra, especially when solving equations. It helps when you want to eliminate coefficients that are in front of a variable, just like in our example \(-4y = 0\).

• To perform division correctly, you need to divide every term in the equation by the number you want to remove. In our case, you divide both sides by \(-4\) to isolate \(y\).
• It's important to remember that division by negative numbers flips the sign of the quotient. However, when zero is involved, as in our equation, zero divided by any non-zero number is still zero.

This means that the operation does not change the value of \(y\) in this instance, so you end up with \(y = 0\). Mastering the concept of division in algebra can greatly simplify your problem-solving process.

Checking your solution is a crucial step in solving algebraic equations. Verifying simply means substituting your solution back into the original equation to ensure the left-hand side equals the right-hand side. In our exercise, the solution found was \(y = 0\). To verify, substitute \(0\) for \(y\) in \(-4y = 0\):

• Substitute the value: \(-4(0)\)
• Simplify the expression to check: \(0 = 0\)

This shows that the solution satisfies the original equation, confirming its correctness. Verification gives you confidence in your result and is a reliable way to avoid mistakes. It's always a good idea to perform this step to ensure your solution is accurate. It can prevent you from accepting incorrect solutions and improve your overall understanding of algebraic equations.