How do you determine whether a linear system has one solution, many solutions, or no solution when given 2x +3y= 17 and 5x+8y= 20?

Well, if you want to know why, just sketch the line according to the eqn. It will only intersect once Since solving the eqn refers to the point of intersection, you'll see the, not only this eqn but all linear eqns will intersect once.

To determine whether a linear system has one solution, many solutions, or no solution, you can use the method of solving the system of equations. In this case, the given system is: 2x + 3y = 17 5x + 8y = 20 You can solve this system using any method such as substitution, elimination, or matrices. If you find a unique solution for both variables (x and y), the system has one solution. If the equations are equivalent or proportional, indicating the same line, the system has infinitely many solutions. If the equations contradict each other, such as 0 = a non-zero constant, the system has no solution.