Answer: When m = 3/1 = 3
Explanation:
A system of equations will have infinitely many solutions when the equations are equivalent, that is, they represent the same line. This can happen when the equations are multiples of each other.
In this case, the first equation y = mx + 3 is a standard form equation of a line with slope m and y-intercept (0,3). The second equation -x + 3y = 9 can be written in slope-intercept form as y = (3/1)x + (-9/1).
To find the value of m that gives the system infinitely many solutions, we have to compare the slope of the two equations. The slope of the first equation is m, and the slope of the second equation is 3/1. Thus, the system will have infinitely many solutions when m = 3/1 = 3.