聯立方程問題2

1.2x+5y+5=0 - (1)
4x+3y+17=0 - (2)

由 (1) : 2x+5y = -5 - (3)
由 (2) : 4x+3y = -17 - (4)
(3) x 2 : 4x+10y= -10 - (5)
(5) - (4) : 7y = 7

把 y = 1 代入 (3)
2x+5 = -5
2x= -10
x= -5

2.2x+3y=18 - (1)
3x+2y=12 - (2)

(1)x2 : 4x+6y=36 - (3)
(2)x3 : 9x+6y =36 - (4)
(4)-(3) : 5x = 0
x=0
把x=0 代入 (3)
y=6

3. 2x+5y-3=0 - (1)
3x-2y+24=0 - (2)

(1) x 3 : 6x+15y-9=0 - (3)
(2) x 2 : 6x-4y+48=0 - (4)
(3)-(4) : 19y-57=0
y = 3
把 y = 3 代入 (4)
6x- 12 + 48 = 0
x = -6

4.(x+4)-2(y-7)=15 - (1)
4(2+x)-3(7-5y)=21 - (2)

由(1) : x+4-2y+14 = 15
x-2y= -3 - (3)
由(2) : 8+4x-21+15y = 21
4x+15y = 34 - (4)
(3)x4 : 4x-8y = -12 - (5)
(4)-(5) : 23y = 46
y = 2
把 y = 2 代入 (3)
x-4= -3
x = 1

5. 3x-(y-10)=0 - (1)
x-2y=0 -(2)

由 (1) : 3x-y = -10 - (3)
(2) x 3 : 3x-6y = 0 - (4)
(3)-(4) = 5y = -10
y = -2
把y = -2 代入 (3)
3x+2= -10
x = -4

(1.)
2x+5y+5=0 => y=(-2x-5)/5
=> y=-0.4x-1
4x+3y+17=0
=> 4x+3(-0.4x-1)+17=0
=> 4x-1.2x-3+17=0
=> 2.8x+14=0
=> x=-14/2.8 = -5
=> y=-0.4(-5)-1 = 2-1 =1

(2.)
2x+3y=18 => y=(18-2x)/3
=> y= 6 -2/3x
3x+2y=12
=> 3x+2(6-2/3x)=12
=> 3x+12-4/3x =12
=> 5/3x=0
=>x=0
=>y=6-2/3(0) =6

(3.)
2x+5y-3=0 => y=(3-2x)/5
=> y=3/5-2/5x
3x-2y+24=0
=> 3x-2(3/5-2/5x)+24 =0
=> 3x-6/5+4/5x+24=0
=> 3.8x+22.8=0
=> x=-22.8/3.8 = -6
=> y= 3/5-2/5(-6) = 3/5+12/5 =3

(4.)
(x+4)-2(y-7)=15 => x+4-2y+14=15
=> x-2y= 15-14-4
=> x = 2y-3
4(2+x)-3(7-5y)=21
=> 8+4x-21+15y=21
=> 4x+15y=21+21-8
=> 4x=34-15y
=> x=(34-15y)/4 =2y-3
=> 34-15y=4(2y-3)
=> 34-15y=8y-12
=> 34+12=15y+8y
=>23y=46
=>y=2
=>x=2(2)-3=1

(5.)
3x-(y-10)=0 => 3x-y+10=0
=> 3x+10=y
x-2y=0
=>x-2(3x+10)=0
=>x-6x-20=0
=> -5x=20
=> x=-4
=> y= 3(-4)+10 =-2

1.
x=-5
y=1
2.
x=0
y=6
3.
x=54/11
y=-15/11
4.
x=-6
y=3
5.
x=-4
y=-2