Question

In the xy-plane, the line y = 2x + b intersects the parabola y = x² + bx + 5 at the point (3, k). If b is a
constant, what is the value of k?

Answer 1

By algebraic handling, the value of k of the system of equations is equal to 2.

What are the values of two constants such that a system of equations has a single solution?

Herein we find a system formed by two equations, a linear function and a quadratic equation with the following characteristics:

y = x² + b · x + 5        (1)

y = 2 · x + b               (2)

If we eliminate y in (1) and (2), then we have this expression:

x² + b · 3 + 5  = 2 · x + b

3² + b · x + 5 = 2 · 3 + b

3 · b + 14 = 6 + b

14 = 6 - 2 · b

8 = - 2 · b

b = - 4

By (2), y = k, x = 3 and b = - 4, we find the value of k:

k = 2 · 3 - 4

k = 6 - 4

k = 2

By algebraic handling, the value of k of the system of equations is equal to 2.

To learn more on systems of equations: https://brainly.com/question/12895249

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