Question 201820: Solve the system of equations:
{ y + 4x = x^2
y + x^2 + 8 = 6x
(___, ___) (___, ___) (___, ___)
Found 2 solutions by Alan3354, RAY100:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! y + 4x = x^2
y + x^2 + 8 = 6x
---------------
y + 4x = x^2 --> y = x^2 - 4x
Sub for y into 2nd eqn
x^2-4x + x^2 + 8 = 6x
2x^2 - 10x + 8 = 0
x^2 - 5x + 4 = 0
(x-4)*(x-1) = 0
x = 1, x = 4
-------------
y = -3, y = 0
------------
(1,-3) is an intserction
(4,0) is another
Answer by RAY100(1637)  (Show Source):
You can put this solution on YOUR website! (1) y+4x = x^2,,,,,,,y = x^2 -4x
.
(2) y+x^2 +8 =6x,,,,,y = -x^2 +6x -8
.
Set (1) =(2)
.
x^2 -4x = -x^2 +6x -8
.
2x^2 -10x +8 =0
.
2(x^2 -5x +4) =0
(x-4)(x-1)=0
.
x= 4, 1
.
in(1) y+4(4) = (4)^2,,,,y=0,,,,,(4,0)
.
y+4(1) = (1)^2,,,,y=-3,,,,,,,,,,,(1,-3)
.
check,,,(1) 0+16=16,,,ok,,,,,,-3 +4 = 1,,,,,ok
(2) 0+16 +8 =24,,,,,ok,,,,,, -3 + 1 +8 =6,,,,ok,,,,,,
|
|
|
