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

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

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

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yes
yes do the substitution and solve for x
with the calculated value for x then put in either original to find y
solving the system means you are finding the (x, y) set that satisfies both equation
yes
Okay. I ended up with y=-0.5({-x+7}-3)^2+8. Is that correct?
yes tht is correct
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@dakid88 no that is not correct
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@Dancingnerd can you continue?
Um. I think so. Then, do i just solve from here?
I ended up with x = -0.5x^2.. It doesn't seem right.
@Dancingnerd do you understand why your expression was wrong?
Oh. It should be x = 0.5x^2.
Yes.
really? how will that give you the value for x ? did you compute that fast?
What do you mean? I think I confused myself.
what equation did you use?
I used -x+7=-0.5(x-3)^2+8.
correct equation
Okay, so how do I solve?
start with the right hand side expand the "exponents" then parenthesis
simplify you will get a quadratic to factor
-x+7=-0.5*x^2+9+8
I have x = 7, x = 1 then find the corresponding values for y
(7, 0) and (-1,6) are the points. Is that correct?
no I have x = 1
That's what I meant. That was the answer that I got.
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Thank you so much! I would have never been able to solve that myself.
any questions ?
I'm still a bit unsure how you got x=7 and x = 1.
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
*did
Ah. Okay.
I think that was where I messed up.
do you understand the process? will you be able to do one by yourself now?

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