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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