Systems of Equations Introduction [When Math Happens Courses]

Summary

A system of equations is a set of two equations with the same variables. Its solution is a set of variable values that makes both equations true at the same time.

Graphically, the solution is the point where the two lines intersect. In the example, the captions appear to show “32,” likely meaning (3, 2). Substituting those values makes both equations true.

Systems of equations can have three types of solutions:

1. One solution: The lines cross at one point.
2. No solution: The lines are parallel and never meet.
3. Infinitely many solutions: The equations look different but represent the same line, so every point on that line is shared.

When solving a system, the goal is to find where the two lines intersect—or determine whether they never intersect or overlap completely.

Speaker/source

One unnamed narrator or instructor.