Question

Find the solutions of the system algebraically.
y=x^2 +1
y =x + 1

Answers

There are no human answers yet.
Answered by GPT 3.5
To solve this system of equations algebraically, we can set the two equations equal to each other and then solve for x:

x^2 + 1 = x + 1

Now, let's rearrange the equation to set it equal to 0:

x^2 + 1 - x - 1 = 0
x^2 - x = 0

Now, factor out an x:

x(x - 1) = 0

Set each factor equal to zero and solve for x:

x = 0
x - 1 = 0
x = 1

Therefore, the solutions to the system of equations are x = 0 and x = 1.

To find the corresponding y-values, we can substitute these x-values back into either of the original equations. Let's choose the equation y = x^2 + 1:

For x = 0,
y = 0^2 + 1
y = 1

For x = 1,
y = 1^2 + 1
y = 2

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

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