Solve the system: y = x4 + 1, y = x2 + 1

To solve the system of equations y = x^4 + 1 and y = x^2 + 1, we need to set the two equations equal to each other because they both equal y.

Step 1: Set the equations equal to each other:

x^4 + 1 = x^2 + 1

Step 2: Subtract x^2 + 1 from both sides to isolate terms with x:

x^4 - x^2 = 0

Step 3: Factor the equation:

x^2(x^2 - 1) = 0

Step 4: Set each factor equal to zero and solve for x:

x^2 = 0 => x = 0

x^2 - 1 = 0 => x^2 = 1 => x = ±1

So, the solutions for x are -1, 0, and 1.

Step 5: Substitute x values into either of the original equations to find the corresponding y values:

For x = -1: y = (-1)^4 + 1 = 2 For x = 0: y = 0^4 + 1 = 1 For x = 1: y = 1^4 + 1 = 2

So, the solutions to the system of equations are (-1, 2), (0, 1), and (1, 2).