Question

已知关于X`Y的方程组｛ax+2by=4 x+y=1与｛x-y=3 bx+(a-1)y=3的解相同，求ab的值

Answer 1

两方程组同解
则说明解同时满足x+y=1,x-y=3
解这个方程组得x=2,y=-1
代回上面得
2a-2b=4,2b+(1-a)=3
解得a=6,b=4
所以ab=24

Answer 2

｛ax+2by=4 x+y=1与｛x-y=3 bx+(a-1)y=3
x+y=1
x-y=3 ，2x=4,x=2,y=-1
ax+2by=4,2a-2b=4,
bx+(a-1)y=3,2b-a+1=3,2b-a=2,a=6,b=4,
ab=4*6=24

Answer 3

x+y=1
x-y=3
解得:X=2 Y=-1
代入AX+2BY=4 BX+(A-1)Y=3
2A+2B*-1=4
2X+(A-1)*-1=3
解方程组得
A=6
B=8

Answer 4

｛ax+2by=4 x+y=1与｛x-y=3 bx+(a-1)y=3 x+y=1 x-y=3 ，2x=4,x=2,y=-1 ax+2by=4,2a-2b=4, bx+(a-1)y=3,2b-a+1=3,2b-a=2,a=6,b=4, ab=4*6=24

Answer 5

x=1-y
1-y-y=3
y=-1
x=2
2a-2b=4
a-b=2
a=2+b
2b-(a-1)=3
2b-a=2
2b-2-b=2
b=4
a=6

Answer 6

x=1-y
1-y-y=3
y=-1
x=2
2a-2b=4
a-b=2
a=2+b
2b-(a-1)=3
2b-a=2
2b-2-b=2
b=4
a=6