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