Graphs of Systems of Equations
🎯 SAT Focus:
The SAT frequently tests your ability to understand what the graph of a system of equations tells you about its solutions. You need to connect the algebraic and graphical representations fluently — and do it fast.
📐 Core Concept: What Is a System of Equations?
A system of equations is a set of two or more equations with the same variables. When we graph these equations on the same coordinate plane, the solution(s) to the system are the point(s) where the graphs intersect.
For two equations $y = f(x)$ and $y = g(x)$, the solution satisfies both equations simultaneously:
$$f(x) = g(x)$$
Each intersection point $(a, b)$ means that when $x = a$, both equations give $y = b$.