Final answer:
The given system of linear equations has no solution because the two lines are parallel, indicated by having the same slope but different y-intercepts.
Step-by-step explanation:
The student has asked, "How many solutions does the system of linear equations below have? 3x + 5y = -9 and -3x + 5y = 9". To determine the number of solutions, we need to analyze the given equations to establish if they represent the same line, parallel lines, or if they intersect at a single point.
Firstly, we can rewrite both equations in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept:
- For 3x + 5y = -9, dividing by 5 gives y = -3/5 * x - 9/5.
- For -3x + 5y = 9, dividing by 5 gives y = 3/5 * x + 9/5.
Comparing the two equations, we see that they have the same slope (-3/5) but different y-intercepts (-9/5 and 9/5, respectively). This means that the lines are parallel and do not intersect at any point, hence there is no solution to the system of equations.