Question

Is (1, 5) a solution to the following system of equations? Explain why or why not.

f(x) = 3x²

g(x) = |x - 1|
1) Yes, because the values of f(1) and g(1) are both equal to 5
2) Yes, because the values of f(1) and g(1) are both equal to 1
3) No, because the values of f(1) and g(1) are not equal
4) Cannot be determined

Answer 1

The point (1, 5) is not a solution to the system of equations f(x) = 3x² and g(x) = |x - 1| because f(1) = 3 and g(1) = 0, which do not both equal 5.

Step-by-step explanation:

The question asks whether the point (1, 5) is a solution to the system of equations given by the functions f(x) = 3x² and g(x) = |x - 1|. To determine this, we evaluate both functions at x = 1 and compare the results to the y-coordinate of the point in question.

For f(x) = 3x², when x = 1, f(1) = 3(1)² = 3. For g(x) = |x - 1|, g(1) = |1 - 1| = 0. Hence, the values of f(1) and g(1) are 3 and 0 respectively, which are not both equal to the y-coordinate 5.

Therefore, the correct answer is option 3): No, because the values of f(1) and g(1) are not equal, and consequently, (1, 5) is not a solution to the system of equations.