To solve the system of equations, we substitute the quadratic equation into the linear equation and analyze the result.

Step 1: Substitute (y = x^2 + 1) into (2x - y = 3)

Replace (y) in the linear equation:
[2x - (x^2 + 1) = 3]

Step 2: Simplify to form a quadratic equation

[2x - x^2 - 1 = 3]
Rearrange terms:
[x^2 - 2x + 4 = 0]

Step 3: Check the discriminant

For (ax^2 + bx + c = 0), the discriminant is (D = b^2 - 4ac):
[D = (-2)^2 - 4(1)(4) = 4 - 16 = -12]

Step 4: Conclusion

Since the discriminant is negative, there are no real solutions to the system.

Answer: No real solutions.

If complex solutions are required:
(x = 1 \pm i\sqrt{3}), (y = -1 \pm 2i\sqrt{3})

But for most basic algebra contexts, the answer is:

(\boxed{\text{No real solutions}})

Or if the problem expects to state no solution in boxed form (as per common practice):

(\boxed{\text{No solution}})

(Note: Depending on the problem's context, "No real solution" is more precise, but "No solution" is often accepted.)

Final Answer
(\boxed{\text{No solution}})

作者声明:本文包含人工智能生成内容。