Is there a value for the slope, , that gives an infinite number of solutions for the following system of equations?If the system of equations has an infinite number of solutions then the equations describe the same line. In other words, the lines have the same slope and y-intercept. If we set the slope, , to , then the lines will have different y-intercepts and therefore will not describe the exact same line.
The lines in the figure are parallel and never intersect. In other words, the equation system above has no solutions. So the final answer to the question will be "no, since the lines have different y-intercepts this system of equations will never have an infinite number of solutions".