Given the graphs of f(x) = 3x − 3 and g(x) = −x + 5, which statements are true? Responses A The system has two solutions.The system has two solutions. B The system has infinitely many solutions.The system has infinitely many solutions. C Point (2, 3) is the only solution.Point (2, 3) is the only solution. D Any point on either line is a solution.Any point on either line is a solution. E The point of intersection is the solution.
The correct statement is E: The point of intersection is the solution.
To find the point of intersection, we need to set f(x) equal to g(x) and solve for x:
3x - 3 = -x + 5
4x = 8
x = 2
Plugging x = 2 back into either equation gives us the corresponding y-coordinate:
f(2) = 3(2) - 3 = 6 - 3 = 3
Therefore, the point of intersection is (2, 3), which is the solution to the system of equations.