1. Let's start by stating the problem: Why does algebra exist? 2. Algebra exists as a branch of mathematics to provide a systematic way to represent and solve problems involving unknown quantities. 3. The fundamental idea in algebra is to use symbols (like $x$, $y$) to represent numbers and express relationships between them using equations and formulas. 4. Algebra allows us to generalize arithmetic operations and solve problems that are not limited to specific numbers but apply to many cases. 5. For example, the formula for solving a linear equation $ax + b = 0$ is $x = -\frac{b}{a}$, which works for any values of $a$ and $b$ (with $a \neq 0$). 6. This generalization helps in fields like science, engineering, economics, and everyday problem-solving by providing tools to model and analyze situations. 7. In summary, algebra exists to help us understand and solve problems involving unknowns in a clear, logical, and general way.