Solve the system y = -x + 7 and y = -0.5(x - 3)^2 + 8. With an explanation would be good! :)

- anonymous

Solve the system y = -x + 7 and y = -0.5(x - 3)^2 + 8. With an explanation would be good! :)

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- cliffordtapp

what is x

- dakid88

x means that and do not represent the same math object (Both symbols do not have the same value). (The forms !=, /= or <> are generally used in programming languages where ease of typing and use of ASCII text is preferred.) x ≈ y means x is approximately equal to y.

- anonymous

So, how would I solve this? Would i substitute y=-x+7 into the second equation?

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## More answers

- jacobciezki

yes

- triciaal

yes do the substitution and solve for x

- triciaal

with the calculated value for x then put in either original to find y

- triciaal

solving the system means you are finding the (x, y) set that satisfies both equation

- dakid88

yes

- anonymous

Okay. I ended up with y=-0.5({-x+7}-3)^2+8. Is that correct?

- dakid88

yes tht is correct

- triciaal

|dw:1441813046839:dw|

- triciaal

@dakid88 no that is not correct

- dakid88

|dw:1441813181344:dw|

- triciaal

@Dancingnerd can you continue?

- anonymous

Um. I think so. Then, do i just solve from here?

- anonymous

I ended up with x = -0.5x^2.. It doesn't seem right.

- triciaal

@Dancingnerd do you understand why your expression was wrong?

- anonymous

Oh. It should be x = 0.5x^2.

- anonymous

Yes.

- triciaal

really? how will that give you the value for x ? did you compute that fast?

- anonymous

What do you mean? I think I confused myself.

- triciaal

what equation did you use?

- anonymous

I used -x+7=-0.5(x-3)^2+8.

- triciaal

correct equation

- anonymous

Okay, so how do I solve?

- triciaal

start with the right hand side expand the "exponents" then parenthesis

- triciaal

simplify you will get a quadratic to factor

- anonymous

-x+7=-0.5*x^2+9+8

- triciaal

I have x = 7, x = 1
then find the corresponding values for y

- anonymous

(7, 0) and (-1,6) are the points. Is that correct?

- triciaal

no I have x = 1

- anonymous

That's what I meant. That was the answer that I got.

- triciaal

##### 1 Attachment

- anonymous

Thank you so much! I would have never been able to solve that myself.

- triciaal

any questions ?

- anonymous

I'm still a bit unsure how you got x=7 and x = 1.

- triciaal

do you follow the directions starting with the right hand side after setting the y's equal?
simplify to the quadratic
I used x^2 - 8 x + 7 = 0

- triciaal

*did

- anonymous

Ah. Okay.

- anonymous

I think that was where I messed up.

- triciaal

do you understand the process? will you be able to do one by yourself now?

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