Final answer:
To solve a system of linear equations algebraically, compare the slopes and y-intercepts of the equations to determine if they have no solution, one solution, or infinitely many solutions.
Step-by-step explanation:
Solving a system of linear equations algebraically involves analyzing each pair of equations to determine if they have no solution, one solution, or infinitely many solutions. The process includes checking for parallel lines (no solution), intersecting lines (one solution), and overlapping lines (infinitely many solutions). For example, equations of the form y = mx + b with different slopes have one point of intersection, while equations with the same slope and y-intercept (identical equations) represent the same line, leading to infinitely many solutions.