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raebaby420
Group Title
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
 11 months ago
 11 months ago
raebaby420 Group Title
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
 11 months ago
 11 months ago

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raebaby420 Group TitleBest ResponseYou've already chosen the best response.0
@Jack1
 11 months ago

mhmdrz91 Group TitleBest ResponseYou've already chosen the best response.0
be 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? ;)
 11 months ago

Jack1 Group TitleBest ResponseYou've already chosen the best response.1
hey @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)
 11 months ago

Jack1 Group TitleBest ResponseYou've already chosen the best response.1
so 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
 11 months ago

Jack1 Group TitleBest ResponseYou've already chosen the best response.1
0 = 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
 11 months ago

Jack1 Group TitleBest ResponseYou've already chosen the best response.1
a * 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)
 11 months ago

Jack1 Group TitleBest ResponseYou've already chosen the best response.1
imagine 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
 11 months ago

Jack1 Group TitleBest ResponseYou've already chosen the best response.1
therefore: 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?
 11 months ago
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