Question

Solve the system by any method. Please show your steps.

y=x+2
y=x^2

Answer 1

Substitute the expression for y from the first equation into the second equation and solve for x. Just as before.

Answer 2

y=x^2+2?

Answer 3

Not quite. From the first equation, we know that y=x+2. So in the second equation, put x+2 in place of y.

Answer 4

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?

Answer 5

So the second equation can be written\[x+2=x ^{2}\]Can you solve this for x?

Answer 6

yesfff

Answer 7

Great. What do you get?

Answer 8

2,-1

Answer 9

Perfect. Now, take of these x-values and substitute them into either of the given equations to solve for y. What do you get?

Answer 10

im not sure what the soultion would be? @ospreytriple

Answer 11

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?

Answer 12

y=x*-1+2 ?

Answer 13

i dont think that correct set up

Answer 14

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?

Answer 15

y=1

Answer 16

That's one solution. What's the other one? (when x=2)

Answer 17

and 4

Answer 18

Excellent. This system of equations has two solutions (-1, 1) and (2, 4). Both these solutions satisfy both equations. Well done.

Answer 19

thank yuoi

Answer 20

You're welcome.