8. Find the solutions of the system algebraically.

Question

y = x^2 + 1
y = x + 1

A. (0, 1) and (1, 2)
B. (0, 1) and (-1, 2)
C. (0, -1) and (1, 2)
D. no solution

Answer 1

To find the solutions algebraically, we can set the two equations equal to each other:

x^2 + 1 = x + 1

Subtract x + 1 from both sides:

x^2 - x = 0

Factor out an x:

x(x - 1) = 0

So the solutions are x = 0 and x = 1.

Now we can substitute these values back into one of the original equations to find the corresponding y values:

For x = 0:
y = 0 + 1 = 1

For x = 1:
y = 1 + 1 = 2

Therefore, the solutions to the system are (0, 1) and (1, 2).

A. (0, 1) and (1, 2)