Systems of Equations in Two Variables
📌 What is a System of Equations?
A system of equations is a set of two or more equations that share the same variables. We write them together using a brace to show they must be solved simultaneously — meaning we need values that satisfy all equations at the same time.
Formal Definition
A system of linear equations in two variables is written as:
$$\begin{cases} a_1x + b_1y = c_1 \\ a_2x + b_2y = c_2 \end{cases}$$
where $a_1, b_1, c_1, a_2, b_2, c_2$ are real number constants, and $x$ and $y$ are the unknown variables.
A solution to the system is an ordered pair $(x, y)$ that makes both equations true simultaneously.