91Ó°ÊÓ

Algebra is a branch of mathematics that deals with symbols and the rules for manipulating these symbols. In simple terms, it's how we use letters to represent numbers in equations, making complex problems simpler to solve. For example, letters like \(x\) and \(y\) often stand in for unknown values we want to find. In algebra, we translate real-world scenarios into mathematical equations and use operations like addition, subtraction, multiplication, and division to solve them. In our exercise, the equation \(2x + y = -8\) is an algebraic equation where - \(x\) and \(y\) are variables representing unknown values. - The equation suggests a relationship between \(x\) and \(y\), meaning the value of one might depend on the other. By using such equations, we can solve real-world puzzles or mathematical problems by systematically manipulating and simplifying expressions.

The substitution method is a popular technique in algebra for solving systems of equations or when one of the variables has been assigned a specific value. It involves replacing a variable with its known value to simplify the equation and make it solvable.Here's how it works:

• Identify which variable has a given value or expression.
• Replace the variable in the equation with this value or expression.
• Proceed to solve the simpler equation that results from this substitution.

In our exercise, we are given \(x = -3\) in the equation \(2x + y = -8\). By substituting \(-3\) for \(x\), we transform the equation into \(2(-3) + y = -8\), making it easier to solve for \(y\). This technique can be especially handy when dealing with several equations and unknowns.

A step-by-step solution in algebra breaks down the process of solving a problem into small, manageable chunks that are easy to follow. This approach helps prevent errors and makes understanding the solution clearer.Consider this exercise:1. **Substitute the Value**: You start by substituting the given \(x \) value into the equation: \( 2(-3) + y = -8 \).2. **Simplify**: Then, you simplify the equation by performing the arithmetic operation: multiply \(2\) and \(-3\) to get \(-6\), leading to \(-6 + y = -8\).3. **Solve for y**: The last step is solving for \(y\). By adding \(6\) to both sides, you arrive at \( y = -2 \).With practice, these steps become second nature, allowing you to tackle more complex problems with confidence.