二元一次(加減法)

1. 3x - y = 7 ....(i)
3x + 2y =13 ....(ii)
3x-7=y
3x +2(3x-7)=13
3x +6x-14=13
9x=13+ 14
x=27/9
x=3
3(3)-7=y
9-7=y
y=2

2. 4x - y =13 ....(i)
2x+ 3y = 3...(ii)
4x-13=y
2x +3(4x-13)=3
2x +12x-39=3
14x=3+ 39
x=42/14
x=3
4(3)-13=y
12-13=y
y=-1

3. 3x+ 2y=1...(i)
x-4y=5 ...(ii)
x=5 +4y
3(5 4y)+ 2y=1
15 +12y +2y=1
14y=1-15
y=-14/14
y=-1
x=5 +4(-1)
x=5-4
x=1

4. 5x+ y+ 7=0....(i)
3x-2y=1 ...(ii)
(i)乘3
15x +3y+ 21=0.....(iii)
(ii)乘5
15x-10y=5.....(ix)
將(iii)減(ix)
13y=26
y=-26/13
y=-2
5x +(-2)+ 7=0
5x +5=0
x=-5/5
x=-1

5. 4x-5y=9...(i)
3x-y-4=0...(ii)
3x-4=y
4x-5(3x-4)=9
4x-15x 20=9
-11x=-20 9
11x=11
x=1
3(1)-4=y
3-4=y
y=-1

6. 2x 3y-7=0...(i)
6x-y-2=0...(ii)
6x-2=y
2x+ 3(6x-2)-7=0
2x +18-6-7=0
2x +5=0
x=-5/2______x=-2又二分之一
6(-5/2)-2=y
-15-2=y
y=-17

7. 3x+ 7y+ 2=0....(i)
2x +3y=3=0....(ii) ____[是否2x 3y-3=0]
(i)乘2
6x 14y+ 4=0....(iii)
(ii)乘3
6x 9y-9=0....(ix)
(iii)減(ix)
5y +13=0
y=-13/5.......y=-2又五分之三
2x +3(-13/5)-3=0
2x-39/5-3=0
2x=(39+ 15)/5
2x=54/5
x=54/5乘1/2
x=27/5
x=5又2/5

7. 3x+7y+2=0....(i)
2x+3y=3....(ii)

(i)*2-(ii)*3:
6x+14y+4=0
-) 6x+9y =9
__________________
5y+4=-9
5y=-13
y=-13/5-----(iii)
Put (iii) into (ii)
2x+3(-13/5)=3
=>2x-39/5=15/5
=>2x =54/5
=> x = 27/5
=5.4
x=5.4,y=-2.6

1)
i-ii 3x - y = 7
3x + 2y =13
y=2
put y-->(i)
3x-2=7
x=3
2)
2x(ii) 4x+6y=6
i-ii 4x - y =13
4x+6y=6
y=-1
put y-->(ii)
2x+3(-1)=2
x=2.5
3)from ii,
x=5+4y-(iii)
put(iii)-->(i)
3(5+4y)+2y=1
14y=-14
y=1
put y-->(ii)
x=5+4(1)
x=9
4) 2x(i)
10x+2y=-14
i+ii
10x+2y=-14
3x-2y=1
x=-2
put x-->(i)
5(-2)+y+7=0
y=3
5) from (ii)
y=3x-4-(iii)
put (iii) to (i)
4x-5(3x-4)=9
x=1
put x-->(ii)
3(1)-y-4=0
y=-1
6) 3x(ii)
18x-3y-6=0
i+ii
2x+3y-7=0
18x-3y-6=0
x=13/20
put x-->ii
6(13/20)-y-2=0
y=1.9
7) 2x+3y=3=0
+3?
-3?
(cannot be done!!)