SOLUTION: If anyone could please help me to solve these four problems it would be awesome! I am extremely lost. Please help! Thanks!! They use the Substituion Method & Addition Method. I can

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: If anyone could please help me to solve these four problems it would be awesome! I am extremely lost. Please help! Thanks!! They use the Substituion Method & Addition Method. I can      Log On


   

Question 430714: If anyone could please help me to solve these four problems it would be awesome! I am extremely lost. Please help! Thanks!! They use the Substituion Method & Addition Method. I can't figure out the solution sets. Thank you!
#1 Substituion Method:
x%2By=1
x%5E2%2Bxy-y%5E2=-11
#2 Substituion Method:
x%5E2%2By%5E2=180
x-y=-6
#3 Addition Method:
2x%5E2%2B3y%5E2-30=0
5x%5E2-7y%5E2-17=0
#4 Addition Method:
x%5E2%2By%5E2=16
y%5E2-3x=16
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
#1 Substituion Method:
x%2By=1 --> y = 1-x
x%5E2%2Bxy-y%5E2=-11
x%5E2%2Bx%281-x%29+-+%281-x%29%5E2=-11
x%5E2+%2B+x+-+x%5E2+-1+%2B+2x+-+x%5E2+=+-11
-x%5E2+%2B+3x+-1+=+-11
x%5E2+-+3x+%2B+10+=+0
(x-5)*(x+2) = 0
x = -2, y = 3 (-2,3)
--------------
x = 5, y = -4 (5,-4)
-----------------------
-----------------------
#2 Substituion Method:
x%5E2%2By%5E2=180
x-y=-6
Similar to #1
-------------------
#3 Addition Method:
2x%5E2%2B3y%5E2-30=0
5x%5E2-7y%5E2-17=0
10x%5E2+%2B+15y%5E2+=+150 1st eqn x 5
10x%5E2+-+14y%5E2+=+34 2nd eqn x 2
------------------------- Subtract
29y%5E2+=+116
y%5E2+=+4
y = +2, -2
Sub for y, find x
There are 4 intersections
------------------
------------------
#4 Addition Method:
x%5E2%2By%5E2=16
y%5E2-3x=16
Similar to #3, just subtract to eliminate y^2 terms