Final answer:
The system of equations has 2 solutions: x = 3 and x = -1.
Step-by-step explanation:
The given system of equations is:
y = 4x + 1
y = x^2 + 4
For a system of equations, the number of solutions can be determined by finding the number of intersection points between the two equations on a graph. In this case, the two equations represent a linear function and a quadratic function. Since a quadratic function can have at most 2 intersection points with a linear function, the system has at most 2 solutions. To find the exact number of solutions, we can set the equations equal to each other and solve for x:
4x + 1 = x^2 + 4
Rearranging the equation gives:
x^2 - 4x - 3 = 0
Factoring or using the quadratic formula, we find:
x = 3 or x = -1
Therefore, the system has 2 solutions, x = 3 and x = -1.