SOLUTION: Hey guys and girls, I have a bit of a problem here I have 50 home work questions that I have to submit by mid-night and I'm in a bit over my head at this point with both my summer

Algebra ->  Algebra  -> Systems-of-equations -> SOLUTION: Hey guys and girls, I have a bit of a problem here I have 50 home work questions that I have to submit by mid-night and I'm in a bit over my head at this point with both my summer       Log On

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Question 201190: Hey guys and girls, I have a bit of a problem here I have 50 home work questions that I have to submit by mid-night and I'm in a bit over my head at this point with both my summer classes and there finals tonight and tomorrow. If any body can help me with a few of these problems I would be very, very greatfull!I have to solve the follwing A,{Y=^X2+4X-5 & Y=-X^2+12X-11] B, {X^2+Y^=193 &X-Y=5} C, {X*Y=45 & 3X-Y=-6} D,{X*Y=8 & X^2+Y^2=65} E, {X+Y=-8 & (X-2)^2+(Y+7)^2=5}
I know this is not normal but I have to be at school to take one of my finals and I,m not too good at the substitution method these questions would probabley take me 2 hours to get the correct solutions not to mention the other 46 problems I have to solve! So if anybody is generous enough to help me with these solutions THANK YOU!!! fyi summer sessions are horrible....
Found 2 solutions by jim_thompson5910, Alan3354:
Answer by jim_thompson5910(28703) About Me  (Show Source):
You can put this solution on YOUR website!
Ok I would love to help you with all of these, but it would take me way too long (you'll see below). So I'm only going to do the first two to get you started.


A)

y=x%5E2%2B4x-5 Start with the first equation.


-x%5E2%2B12x-11=x%5E2%2B4x-5 Plug in y=-x%5E2%2B12x-11


-x%5E2%2B12x-11-x%5E2-4x%2B5=0 Get all terms to the left side.


-2x%5E2%2B8x-6=0 Combine like terms.


Notice that the quadratic -2x%5E2%2B8x-6 is in the form of Ax%5E2%2BBx%2BC where A=-2, B=8, and C=-6


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%288%29+%2B-+sqrt%28+%288%29%5E2-4%28-2%29%28-6%29+%29%29%2F%282%28-2%29%29 Plug in A=-2, B=8, and C=-6


x+=+%28-8+%2B-+sqrt%28+64-4%28-2%29%28-6%29+%29%29%2F%282%28-2%29%29 Square 8 to get 64.


x+=+%28-8+%2B-+sqrt%28+64-48+%29%29%2F%282%28-2%29%29 Multiply 4%28-2%29%28-6%29 to get 48


x+=+%28-8+%2B-+sqrt%28+16+%29%29%2F%282%28-2%29%29 Subtract 48 from 64 to get 16


x+=+%28-8+%2B-+sqrt%28+16+%29%29%2F%28-4%29 Multiply 2 and -2 to get -4.


x+=+%28-8+%2B-+4%29%2F%28-4%29 Take the square root of 16 to get 4.


x+=+%28-8+%2B+4%29%2F%28-4%29 or x+=+%28-8+-+4%29%2F%28-4%29 Break up the expression.


x+=+%28-4%29%2F%28-4%29 or x+=++%28-12%29%2F%28-4%29 Combine like terms.


x+=+1 or x+=+3 Simplify.


So the solutions for "x" are x+=+1 or x+=+3



-----------------------------------------------------------


Let's find the value of "y" when x=1


y=x%5E2%2B4x-5 Go back to the first equation.


y=%281%29%5E2%2B4%281%29-5 Plug in x+=+1


y=1%2B4%281%29-5 Square 1 to get 1


y=1%2B4-5 Multiply


y=0 Combine like terms.


So when x+=+1, y=0 giving the ordered pair (1,0)


--------------


Let's find the value of "y" when x=3


y=x%5E2%2B4x-5 Go back to the first equation.


y=%283%29%5E2%2B4%283%29-5 Plug in x+=+3


y=9%2B4%283%29-5 Square 3 to get 9


y=9%2B12-5 Multiply


y=16 Combine like terms.



So when x+=+3, y=16 giving the ordered pair (3, 16)



=======================================================================

Answer:


So the 2 ordered pair solutions are:

(1,0) and (3,16)


B)

x-y=5 Start with the second equation.


x=5%2By Add "y" to both sides.


x%5E2%2By%5E2=193 Move onto the second equation.


%285%2By%29%5E2%2By%5E2=193 Plug in x=5%2By


25%2B10y%2By%5E2%2By%5E2=193 FOIL


25%2B10y%2By%5E2%2By%5E2-193=0 Subtract 193 from both sides.


2y%5E2%2B10y-168=0 Combine like terms.


Notice that the quadratic 2y%5E2%2B10y-168 is in the form of Ay%5E2%2BBy%2BC where A=2, B=10, and C=-168


Let's use the quadratic formula to solve for "y":


y+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


y+=+%28-%2810%29+%2B-+sqrt%28+%2810%29%5E2-4%282%29%28-168%29+%29%29%2F%282%282%29%29 Plug in A=2, B=10, and C=-168


y+=+%28-10+%2B-+sqrt%28+100-4%282%29%28-168%29+%29%29%2F%282%282%29%29 Square 10 to get 100.


y+=+%28-10+%2B-+sqrt%28+100--1344+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-168%29 to get -1344


y+=+%28-10+%2B-+sqrt%28+100%2B1344+%29%29%2F%282%282%29%29 Rewrite sqrt%28100--1344%29 as sqrt%28100%2B1344%29


y+=+%28-10+%2B-+sqrt%28+1444+%29%29%2F%282%282%29%29 Add 100 to 1344 to get 1444


y+=+%28-10+%2B-+sqrt%28+1444+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


y+=+%28-10+%2B-+38%29%2F%284%29 Take the square root of 1444 to get 38.


y+=+%28-10+%2B+38%29%2F%284%29 or y+=+%28-10+-+38%29%2F%284%29 Break up the expression.


y+=+%2828%29%2F%284%29 or y+=++%28-48%29%2F%284%29 Combine like terms.


y+=+7 or y+=+-12 Simplify.


So the solutions (for "y") are y+=+7 or y+=+-12


------------------------------------------------------------


Let's find the value of "x" when y+=+7


x=5%2By Go back to the previously isolated equation


x=5%2B7 Plug in y+=+7


x=12 Add


So when x=12, y=7. This means that we have the ordered pair (12, 7)



-----------------------------


Let's find the value of "x" when y+=+-12


x=5%2By Go back to the previously isolated equation


x=5-12 Plug in y+=+-12


x=-7 Subtract


So when x=-7, y=-12. This means that we have the ordered pair (-7, -12)



=======================================================================

Answer:


So the 2 ordered pair solutions are:

(12, 7) and (-7, -12)

Answer by Alan3354(31507) About Me  (Show Source):
You can put this solution on YOUR website!
A,{Y=^X2+4X-5 & Y=-X^2+12X-11
I assume you want to find the values of x common to these 2 eqns, where they intersect.
Since they both = y, they equal each other.
X^2+4X-5 = -X^2+12X-11
2x^2 - 8x + 6 = 0
(2x - 2)*(x - 3) = 0
x = 3
x = 1
-------
x = 3 --> y = 16 gives the point (3,16)
x = 1 --> y = 0 gives the point (1,0)
These are the 2 points of intersection of the 2 functions.
------------------------
B, X^2+Y^2=193 &X-Y=5
x = y+5
(y+5)^2 + y^2 = 193
y^2 + 10y + 25 + y^2 = 193
2y^2 + 10y - 168 = 0
y^2 - 5y - 84 = 0
(y-12)*(y+7) = 0
y = -7
y = 12
Sub and solve for x as in the 1st one.
--------------------------------------
C X*Y=45 & 3X-Y=-6
y = 3x+6
x*(3x+6) = 45
x^2 + 2x - 15 = 0
(x+5)*(x-3) = 0
x = 3
x = -5
------------
D X*Y=8 & X^2+Y^2=65
Similar to B but with 4 points of intersection.
---------------
E X+Y=-8 & (X-2)^2+(Y+7)^2=5
More of the same
email me via the thank you note if you want me to check your work.