Key Concepts
- A system of linear equations consists of two equations with two variables.
- The solution to a system is the point(s) where both equations are satisfied.
- Types of solutions:
- One solution: The lines intersect at a single point.
- No solution: The lines are parallel and never intersect.
- Infinitely many solutions: The equations represent the same line.
- Finding the number of intersection points can be done algebraically by checking slopes.
Skills Covered
- Recognizing different solution types based on equation properties.
- Understanding what a solution means in the xy-plane.
- Identifying the number of intersection points from equations.
Example Problem
Does the system of equations below have one solution, no solution, or infinitely many solutions? (y = 2x + 3) (4x - 2y = -6)