聯立二元一次方程

(1) x + 2y = 8 ... (1)
x + y = 6 ... (2)
(1) - (2) => y = 2
Sub into (2), x + 2 = 6 => x = 4
(2) -6x + 4y = 21 ...(1)
6x + 8y = 15 ... (2)
(1) + (2) => 12y = 36
y = 3
Sub into (2), 6x + 8*3 = 15
6x = -9
x = -3/2
(3) x - 2y = 6 ... (1)
2x + 3y = 5...(2)
(1) => x = 6 + 2y ... (3)
Sub into (2),
2(6 + 2y) + 3y = 5
12 + 4y + 3y = 5
7y = -7
y = -1
Sub into (3), x = 6 - 2 = 4
(4) 4x + 2y = 8 ...(1)
-x + 3y = -9 ...(2)
(2) => x = 3y + 9 ... (3)
Sub into (1), 4(3y + 9) + 2y = 8
12y + 36 + 2y = 8
14y = -28
y = -2
Sub into (3), x = (3)(-2) + 9 = 3
(5) 設展明今年x歲,媽媽y歲
y - x = 22 ... (1)
y + 2 = 3(x + 2) ... (2)
(1) => y = 22 + x
Sub into (2), 22 + x + 2 = 3(x + 2)
24 + x = 3x + 6
2x = 18
x = 9
展明今年9歲

just try:P
5.媽媽與展明的年齡相差22歲. 2年後,媽媽的年齡是展明的3倍,問展明今年多少歲?
展明=X
so:媽媽=X+22
2年後:
展明=X+2
so:媽媽=X+24
媽媽的年齡是展明的3倍:3(X+2)=媽媽
so:
3(x+2)=x+24
3x+6=x+24
3X=x+18
2X=18
x=9

展明今年9歲
answer 1 is right and this don't need to use聯立二元一次方程=_=

2010-01-01 13:49:03 補充：
and y answer 2 is wrong:P
5.設媽媽的年齡為x
設展明的年齡為y
x-y=22-----(1)=ok
x+2=3y----(2)=wrong , 2年後媽媽+2 ,展明+0 -,-?

right answer: x+2=3(y+2)


x=y+22----(3)=same as (1)=_=

do maths need to be more careful:P

1.
x+2y=8-----(1)
x+y=6-------(2)
x=8-2y------(3)
把(3)代入(2)
8-2y+y=6
8-6=y
y=2
代y=2入(1)
x+2(2)=8
x=4
2.
-6x+4y=21-------(1)
6x+8y=15--------(2)
4y=21+6x
y=(21+6x)÷4----(3)
代(3)入(2)
6x+8x(21+6x)÷4=15
6x+2(21+6x)=15
6x+42+12x=15
18x=-27
x=-27÷18
代x=-27÷18入(1)
-6(-27÷18)+4y=2l
9+4y=21
4y=12
y=3
3.
x-2y=6-------(1)
2x+3y=5----(2)
x=6+2y-----(3)
代(3)入(2)
2(6+2y)+3y=5
12+4y+3y=5
7y=-7
y=-1
代y=-1入(1)
x-2(-1)=6
x=4

4. 4x+2y=8------(1)
-x+3y=-9---------(2)
2y=-4x+8
y=-2x+4------(3)
代(3)入(2)
-X+3(-2x+4)=-9
-x-6x+12=-9
-7x=-21
x=3
代x=3入(1)
4(3)+2y=8
12+2y=8
2y=-4
y=-2
5.設媽媽的年齡為x
設展明的年齡為y
x-y=22-----(1)
x+2=3y----(2)
x=y+22----(3)
代(3)入(2)
y+22+2=3y
24=2y
y=12
代y=12入(1)
x-12=22
x=34
展明今年是12歲.