A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 2 years ago
Please help.
What are the solutions to the following system of equations?
y = x2 + 12x + 30
8x − y = 10
(−4, −2) and (2, 5)
(−2, −4) and (2, 5)
(−2, −4) and (5, 2)
No Real Solutions
anonymous
 2 years ago
Please help. What are the solutions to the following system of equations? y = x2 + 12x + 30 8x − y = 10 (−4, −2) and (2, 5) (−2, −4) and (2, 5) (−2, −4) and (5, 2) No Real Solutions

This Question is Closed

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0be unique y in second equation, then plug in to first equation... in seceon 8x  y = 10 > y = 8x  10 now plug in it to first equation and find x... y = x2 + 12x + 30 > 8x  10 = x2 +12x + 30 got it lady? ;)

Jack1
 2 years ago
Best ResponseYou've already chosen the best response.3hey @raebaby420 , sorry bout the "issues" last time anyway, as @mhmdrz91 said use the second equation to find what y equals (in terms of x) then sub in that result into the first equation (as per post above, cheers mhmd)

Jack1
 2 years ago
Best ResponseYou've already chosen the best response.3so you'll get: 8x  10 = x^2 +12x + 30 now combine "like terms" so 8x = x^2 + 12x + 30 +10 8x = x^2 + 12x + 40 continuing: 0 = x^2 + 12x 8x + 40 >0 = x^2 + 4x + 40

Jack1
 2 years ago
Best ResponseYou've already chosen the best response.30 = x^2 + 4x + 40 from here you've got two options: 1. the quadratic formula (google it, whay too long to type) or 2. factor above equation so: 0 = x^2 + 4x + 40 = (x + a ) ( x + b ) now solve for a and b

Jack1
 2 years ago
Best ResponseYou've already chosen the best response.3a * b = 40 ax + bx = 4x, so a + b = 4 now those 2 equations dont make any sense (as no 2 rational numbers both add to equal 4 and multiply to equal 40) so answer is: no real solution (d)

Jack1
 2 years ago
Best ResponseYou've already chosen the best response.3imagine for a second that the first equation was: y = x^2 + 18x + 30 and the 2nd equation was: y  4x = 10 so rearrange eqn 2: y = 4x  10 sub that into eqn 1 then you would get: y = x^2 + 18x + 30 4x  10 = x^2 + 18x + 30 4x = x^2 + 18x + 30 +10 4x = x^2 + 18x + 40 0 = x^2 + 14x + 40 > 0 = x^2 + 14x + 40 IS an equation that is solvable via factoring proof: 0 = x^2 + 14x + 40 0 = (x + a) ( x + b) now (from FOIL) a * b must equal 40 and a + b must equal 14 so the numbers that match that are 4 and 10 a * b = 40 = 4 *10 a + b = 14 = 4 + 10

Jack1
 2 years ago
Best ResponseYou've already chosen the best response.3therefore: 0 = x^2 + 14x + 40 0 = (x + a) ( x + b) 0 = (x + 4) (x + 10) so (x + 4) times (x + 10) = zero now the only thing that multiplies to equal zero is...ZERO so either (x + 4) = 0 [ as 0 times (x +10) = 0 ] which would mean that x = 4 (x + 4) = 0 (4 + 4) = 0 0 = 0 proof OR (x + 10) = 0 [ as 0 times (x + 4) = 0 ] which would mean that x = 10 (x + 10) = 0 (10 + 10) = 0 0 = 0 proof so there are really 2 answers to "what is x?" 1. if x = 4, (using our new 2nd equation) y  4(x) = 10 y  4 ( 4) = 10 y + (16) = 10 y = 10 16 y = 26 giving coordinates of (4, 26) [ as (x, y) ] or if x = 10 (also using the 2nd equation) y  4(x) = 10 y  4 (10) = 10 y + 40 = 10 y = 50 giving coordinates of (10, 50) [ as (x, y) ] hope this helps?
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.