Final answer:
To decide if a system of equations has a single, many, or no solutions you need to analyze and solve them analytically or graphically. Analytical methods are usually more accurate than graphical ones. Identifying knowns and unknowns, and solving the relevant equations are vital steps in this process.
Step-by-step explanation:
To determine if a system of equations has one solution, no solution, or infinitely many solutions, you must examine the equations in question. If two equations represent different lines that intersect at one point, there is one solution. If the equations represent the same line, there are infinitely many solutions. However, if the equations represent parallel lines, which means they never intersect, there is no solution.
You can also solve a system of equations graphically by plotting the lines and looking for intersections. Nevertheless, the analytical technique of solving algebraically by substitution or elimination is typically more accurate. Graphing relies on the precision of drawing or the resolution of the graphical display, whereas analytical methods provide exact answers.
Summary of Problem Solving involves determining the knowns and unknowns, finding an equation that expresses the unknown in terms of the knowns, and then solving the equation or equations. This process is crucial in understanding whether there exists a single solution, many, or none.