SOLUTION: I might not have the topic exactly right, but I have an issue. This assignment was due today, but it's something I'm really struggling on. It's one of those really long problems th

Algebra ->  Expressions-with-variables -> SOLUTION: I might not have the topic exactly right, but I have an issue. This assignment was due today, but it's something I'm really struggling on. It's one of those really long problems th      Log On


   

Question 1177406: I might not have the topic exactly right, but I have an issue. This assignment was due today, but it's something I'm really struggling on. It's one of those really long problems that take an eternity to figure out.
(x-1)^2+(y+1)^2 = 50
-x+y = -10
I decided to start by solving for y since I'm not a huge fan of too many negatives and I didn't know how to procede with a -x, although it's coming to me now. In the end, when I couldn't go any further, I ended up with 2x^2-24x+72=0, but I can't find anything that multiplies to be 72 and adds to be -24, so I KNOW I made a mistake somewhere, I just can't figure out where. Thank you for your time. :)
Found 4 solutions by josgarithmetic, Edwin McCravy, MathLover1, ikleyn:
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
WHAT are you trying to do? What QUESTION do you hope to answer? Are you looking for solution for the system?

system%28%28x-1%29%5E2%2B%28y%2B1%29%5E2+=+50%2C-x%2By+=+-10%29


The negative 1 coefficient on x in the second equation should be no trouble - none.

-x%2By=-10
y=x-10
-
SUBSTITUTE:
%28x-1%29%5E2%2B%28x-10%2B1%29%5E2=50
%28x-1%29%5E2%2B%28x-9%29%5E2=50
x%5E2-2x%2B1%2Bx%5E2-18x%2B81-50=0


Can you continue from here, solve for x, and then continue on?

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
The other tutor made a mistake and got 31 where he should have gotten 32,
because he forgot to add the 1 to 81 in the previous step.


system%28%28x%5E%22%22-1%29%5E2%2B%28y%5E%22%22%2B1%29%5E2+=+50%2C-x%2By+=+-10%29

Solve the second for y:

y=x-10

Substitute in the first

%28x%5E%22%22-1%29%5E2%2B%28%28x%5E%22%22-10%29%5E%22%22%2B1%29%5E2+=+50

%28x%5E%22%22-1%29%5E2%2B%28x%5E%22%22-10%5E%22%22%2B1%29%5E2+=+50

%28x%5E%22%22-1%29%5E2%2B%28x%5E%22%22-9%5E%22%22%29%5E2+=+50



%28x%5E2-x-x%2B1%29%2B%28x%5E2-9x-9c%2B81%29=50

%28x%5E2-2x%2B1%29%2B%28x%5E2-18x%2B81%29=50

x%5E2-2x%2B1%2Bx%5E2-18x%2B81=50

2x%5E2-20x%2B82=50

2x%5E2-20x%2B32=0

Divide every term by 2

2x%5E2%2F2-20x%2F2%2B32%2F2=0%2F2

x%5E2-10x%2B16=0

%28x-2%29%28x-8%29=0

x-2=0;  x-8=0
  x=2;    x=8

Find the y-value that goes with x=2

y=x-10
y=2-10
y=-8

So one solution is (x,y) = (2,-8)

Find the y-value that goes with x=8

y=x-10
y=8-10
y=-2

So the other solution is (x,y) = (8,-2)

The graph looks like this, The 2 solutions are the coordinates of the points
where the graphs of the two equations intersect:

  

Edwin

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

%28x-1%29%5E2%2B%28y%2B1%29%5E2+=+50................1)
-x%2By+=+-10........................2)
----------------------------------------------------
%28x-1%29%5E2%2B%28y%2B1%29%5E2+=+50................1) expand
x%5E2-2x%2B1%2By%5E2%2B2y%2B1+=+50
x%5E2-2x%2B1%2By%5E2%2B2y%2B1+-50=0
x%5E2-2x%2By%5E2%2B2y+-48=0............1a

-x%2By+=+-10........................2), solve for y
y+=x+-10........................, substitute in 1a
x%5E2-2x%2B%28x+-10%29%5E2%2B2%28x+-10%29+-48=0
x%5E2-2x%2Bx%5E2+-20x%2B100%2B2x+-20-48=0
2x%5E2+-20x%2B32=0....simplify
x%5E2+-10x%2B16=0
%28x+-+8%29+%28x+-+2%29+=+0
=> x=8 or x=2
go to
-x%2By+=+-10........................2), substitute x=8
-8%2By+=+-10
y+=+-10%2B8
y+=+-2
or
-x%2By+=+-10........................2), substitute x=2
-2%2By+=+-10
y+=+-10%2B2
y+=+-8
Solutions:
x=8,y+=+-2
x=2, y+=+-8

Answer by ikleyn(52767) About Me  (Show Source):
You can put this solution on YOUR website!
.

In the lesson

    - Solving systems of algebraic equations of degree 2 and degree 1

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