Question
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.
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GPT 3.5
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.
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.
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