Find the solutions of the system algebraically.

Question

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

Answer 1

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).