一道一元一次方程式數學題

a(2x-3) - 4x - 2y + 9 = by + c

- 4x - 2y + 9 = - a(2x-3) + by + c

- a(2x-3) + by + c = - 4x - 2y + 9


使 - a(2x-3) + by + c = a+b+c

所以 -a(2x-3) = a , by = b

-a(2x-3) = a , 則 -2x+3=1 , x=1

by = b , y=1


將 x=1 , y=1 代入 - a(2x-3) + by + c = - 4x - 2y + 9

則 a+b+c = -4-2+9 = 3

不需要什麼長篇大論的解釋
觀念就是多項式相等而已~

小紅茶解釋的非常清楚good

a(2x-3)-4x-2y+9=by+c
2ax-3a-4x-2y+9=by+c
(2a-4)x-2y+(9-3a)=by+c

x係數：
(2a-4)x=0x
→ 2a-4=0, 2a=4, a=2

y係數：
-2y=by
→ -2=b, b=-2

常數項：
(9-3a)=c
→ a=2代入, (9-6)=c, c=3

a+b+c=2+(-2)+3=3

a(2x-3)-4x-2y+9=by+c
-->2ax-3a-4x-2y+9=by+c
-->(2a-4)x-(3a+2)y+9=by+c
-->2a-4=0 , -(3a+2)=b , 9=c
-->a=2 , b=-(3*2+2)=-8 , c=9