Solve the system by any method. Please show your steps. y=x+2 y=x^2

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Solve the system by any method. Please show your steps. y=x+2 y=x^2

Mathematics
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Substitute the expression for y from the first equation into the second equation and solve for x. Just as before.
y=x^2+2?
Not quite. From the first equation, we know that y=x+2. So in the second equation, put x+2 in place of y.

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The important point here is to recognize the meaning of the equals sign(=). The equation y=x+2 means that y and x+2 are exactly the same. That means that wherever we have y, we could replace it with x+2 and vice versa. Make sense?
So the second equation can be written\[x+2=x ^{2}\]Can you solve this for x?
yesfff
Great. What do you get?
2,-1
Perfect. Now, take of these x-values and substitute them into either of the given equations to solve for y. What do you get?
im not sure what the soultion would be? @ospreytriple
Sorry, was away for a sec. Take the first equation, y=x+2. Evaluate it for x=2 and for x=-1. There will be two solutions. What are they?
y=x*-1+2 ?
i dont think that correct set up
There is no need to use the variable x any more. You've already determined the value of x. Remember the meaning of the equals sign. By saying x=2, that means that we can replace x with 2. So the first equation becomes y=2+2 for x=2 and it becomes y=-1+2 for x=-1. Now, what do you get for y?
y=1
That's one solution. What's the other one? (when x=2)
and 4
Excellent. This system of equations has two solutions (-1, 1) and (2, 4). Both these solutions satisfy both equations. Well done.
thank yuoi
You're welcome.

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