中4 數學.解聯立方程,唔該大家列詳細少少,唔該大家啊 ^^

2/y -x=1---------------1
x - 4y=1-----------------2
For 1,
2 - xy = y--------------3
For 2,
x = 1 - 4y--------------4
Put 4 into 3,
2 - (1- 4y)y = y
2 - y + 4y ^2 = y
4y ^2 - 2y + 2 = 0
2y ^2 - y + 1 = 0
(2y + 1)(y - 1) = 0
y = -1/2 or y = 1
Put y = -1/2 into 4,
x = 1 - 4(-1/2)
x = 3
Put y = 1 into 4,
x = 1 - 4(1)
x = -3
So, x = 3 , y = -1/2 OR x = -3 , y = 1




x^2 - 2y^2 = 3x+4y--------------1
3x + 4y=1-------------------------2
Put 2 into 1,
x ^2 - 2y ^ 2 = 1
x ^2 - 2y ^ 2 - 1 ^2 = 0
(x - 2y - 1)(x + 2y + 1) = 0
x = 1 + 2y or x = - 1 - 2y
Put x = 1 + 2y into 2,
3(1 + 2y) + 4y = 1
3 + 6y + 4y = 1
10y = -2
y = -5
Put x = - 1 - 2y into 2,
3(-1 - 2y) + 4y = 1
- 3 - 6y + 4y = 1
- 3 - 2y = 1
- 2y = 4
y = - 2
Put y = -5 into 2,
3x + 4(-5) = 1
3x - 20 = 1
3x = 21
x = 7
Put y = -2 into 2,
3x + 4(-2) = 1
3x - 8 = 1
3x = 9
x = 3
So, x = 7 , y = - 5 OR x = 3 , y = - 2

有2條
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2/y -x=1---------------1
x - 4y=1-----------------2

(1) X = 2/Y - 1
(2) X = 1 + 4Y

SUB (1) into (2)

2/Y - 1 = 1 + 4Y

4Y^2 + 2Y - 2 = 0

2Y^2 + Y - 1 = 0

(2Y - 1)( Y + 1) = 0

Y=1/2 or Y= -1

when Y = 1/2,

X - 4(1/2) = 1

X = 3

when Y = -1

X - 4(-1) = 1

X + 4 = 1

X = -3

*************************************

x^2 - 2y^2 = 3x+4y--------------1
3x + 4y=1-------------------------2

---------------------------
SUB 2 INTO 1

X^2 - 2Y^2 = 1 ------------(3)
----------------------------

FROM 2,

X = (1 - 4Y) / 3 <--- put in into (3)

[(1 - 4Y) / 3 ]^2 - 2Y^2 = 1

(1 - 4Y)^2 / 9 - 2Y^2 = 1

( 1 - 8Y + 16Y^2 ) - 18Y^2 = 9

2Y^2 + 8Y + 8 = 0

Y^2 + 4Y + 4 = 0

Y = -2


when Y = -2

3X + 4(-2) = 1

3X = 9

X = 3

2/y - x = 1...(1)
x - 4y = 1...(2)
from (2)
x = 1 + 4y
sub x = 1+4y into (1)
2/y - (1+4y) = 1
2/y - 1 - 4y = 1
2/y - 4y = 2
1/y - 2y = 1
1 - 2y^2 = y
2y^2 + y - 1 = 0
(2y-1)(y+1) = 0
2y - 1 = 0 or y+1 = 0
y = 1/2 or y = -1
when y = 1/2
2/y - x = 1...(1)
2/(1/2) - x = 1
4 - x = 1
x = 3
therefore, x = 3, y = 1/2
when y = -1
x - 4y = 1 ...(2)
x - 4(-1) = 1
x + 4 = 1
x = -3
therefore, x = -3, y = -1//

x^2 - 2y^2 = 3x + 4y...(1)
3x + 4y = 1...(2)
from (1) and (2)
x^2 - 2y^2 = 1...(3)
from (2)
x = (1-4y)/3...(4)
sub (4) into (3)
[(1-4y)/3]^2 - 2y^2 = 1
(1-4y)^2 /9 - 2y^2 = 1
(1-8y+16y^2) / 9 - 2y^2 = 1
1 - 8y + 16y^2 - 18y^2 = 9
-8y - 2y^2 - 8 = 0
y^2 + 4y + 4 = 0
(y+2)^2 = 0
y+2 = 0 (repeated)
y = -2
sub y = -2 into (2)
3x + 4y = 1
3x + 4(-2) = 1
3x - 8 = 1
x = 3

therefore, x = 3, y = -2//

1. (1)+(2) 2/y-4y=2
2-4y^2=2y
4y^2+2y-2=0
2y^2+y-1=0
(2y-1)(y+1)=0
y=1/2 or y=-1
when y=1/2 x=3
y=-1 x=-3