聯立方程 加減消元方(請盡快回答)

1.
{m - n = 2......①
{m + n = - 2....②

① + ② gives 2m = 0, so m = 0.
② - ① gives 2n = -4, so n = -2.

{m = 0
{n = -2


2.
{x + 3y = 5....①
{x + 2y = 3....②

① - ② gives y = 2.
Put into ②:
x + 2(2) = 3
x = 3 - 4 = -1

{x = -1
{y = 2


3.
{5m + 2n = 8...①
{3m - 2n = 8....②

① + ② gives 8m = 16, so m = 2.
Put into ①:
5(2) + 2n = 8
2n = 8 - 10 = -2
n = -1

{m = 2
{n = -1


4.
{4x - 3y = 2.....①
{-3y + x = 5.....②

① - ② gives 3x = -3, then x = -1.
Put into ①:
4(-1) - 3y = 2
3y = -4 - 2 = -6
y = -2

{x = -1
{y = -2


5.
{3x + 5y = 5....①
{x + 3y = 3.....②

② × 3: 3x + 9y = 9 ... ③
③ - ① gives 4y = 4, then y = 1.
Put into ①:
3x + 5(1) = 5
x = 0

{x = 0
{y = 1


6.
{2x - y = 3......①
{5x - 3y = 4.....②

① × 3: 6x - 3y = 9 ... ③
③ - ② gives x = 5.
Put into ①:
2(5) - y = 3
10 - y = 3
y = 7

{x = 5
{y = 7


7.
{x + 3y = 1....①
{5x + y = 6....②

② × 3: 15x + 3y = 18 ... ③
③ - ① gives 14x = 17, then x = 17/14.
Put into ①:
17/14 + 3y = 1
3y = -3/14
y = -1/14

{x = 17/14
{y = -1/14


2015-01-18 16:29:19 補充：
ho Pui，不好意思，你的第六題應該有誤。

因為 15 - 8 = 7。

1.
m-n=2......(1)
m+n= -2....(2)
(1)+(2),2m=0
m=0
代m=0入(2)
n=-2

2.
x+3y=5....(1)
x+2y=3....(2)
(1)-(2),y=2
代y=2入(1)
x+6=5
x=-1

3.
5m+2n=8...(1)
3m-2n=8....(2)
(1)+(2)
8m=16
m=2
代m=2入(1)
10+2n=8
n=-1

4.
4x-3y=2.....(1)
-3y+x=5.....(2)
(1)-(2),3x=-3
x=-1
代x=-1入(2)
-3y-1=5
y=-2

5.
3x+5y=5....(1)
x+3y=3.....(2)
3*(2),3x+6y=9...(3)
(3)-(1)y=4
代y=4入(2)
x+3*4=3
x=-9

6.
2x-y=3......(1)
5x-3y=4.....(2)
3*(1),6x-3y=9...(3)
(3)-(2),x=5
代x=5入(1)
10-y=3
y=7

7.
x+3y=1....(1)
5x+y=6....(2)
3*(2),15x+3y=18...(3)
(3)-(1),14x=17
x=17/14
代x=17/14入(1)
17/14+3y=1
y=-1/14

1.m-n=2......(1)
m+n=2....(2)

(1)+(2)
2m=0
m=0

0-n=2
0=2+n
n=-2

2. x+3y=5....(1)
x+2y=3....(2)

(1)-(2)
y=2
x+2(2)=3
x+4=3
x=-1

3. 5m+2n=8...(1)
3m-2n=8....(2)

(1)+(2)
8m=16
m=2

5(2)+2n=8

10+2n=8
2n=-2
n=-1

4.4x-3y=2.....(1)
x-3y=5.....(2)

(1)-(2)
3x=-3
x=-1

-1-3y=5
-3y=6
y=-2

5. 3x+5y=5....(1)
x+3y=3.....(2)

3(x+3y)=3(3).....(2)
3x+9y=9......(3)

(3)-(1)
4y=4
y=1

3x+5(1)=5
3x+5=5
3x=0
x=0

6. 5(2x-y)=3(5)......(1)
10x-5y=15......(3)

2( 5x-3y)=4(2).....(2)
10x-6y=8.....(4)

(3)-(4)
y=-7

2x-(-7)=3

2x+7=3
2x=-4
x=-2

7. x+3y=1....(1)
3(5x+y)=6(3)....(2)
15x+3y=18....(3)

(3)-(1)
14x=17
x=17/14

(17/14)+3y=1
17+42y /14=1
17+42y =14
42y =-3
y=-1/14