解方程组2(x-1)-3(y+2)=1 3(x-1)+5(y+2)=12.9

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解方程组2(x-1)-3(y+2)=13(x-1)+5(y+2)=12.9解方程组2(x-1)-3(y+2)=13(x-1)+5(y+2)=12.9解方程组2(x-1)-3(y+2)=13(x-1)+

解方程组2(x-1)-3(y+2)=1 3(x-1)+5(y+2)=12.9
解方程组2(x-1)-3(y+2)=1 3(x-1)+5(y+2)=12.9

解方程组2(x-1)-3(y+2)=1 3(x-1)+5(y+2)=12.9
2(x-1)-3(y+2)=1
2x-2-3y-6=1
2x-3y=1+2+6
2x-3y=9(1)
3(x-1)+5(y+2)=12.9
3x-3+5y+10=12.9
3x+5y=12.9+3-10
3x+5y=5.9(2)
(1)*5得:10x-15y=45(3)
(1)*3得:9x+15y=17.7(4)
(3)+(4)得:19x=62.7
x=3.3
将x=3.3带入(1)得:2*3.3-3y=9
y=-0.8
所以方程组的解为x=3.3,y=-0.8

令a=x-1
b=y+2
所以
2a-3b=1 (1)
3a+5b=12.9 (2)
(1)×5+(2)×3
10a+9a=5+38.7
19a=43.9
a=439/190
b=(12.9-3a)/5=334/285
所以
x=a+1=629/190
y=b-2=-236/285

将方程式2(x-1)-3(y+2)=1扩大3倍,得6(x-1)-3(y+2)=3 (3)
将方程式3(x-1)+5(y+2)=12.9扩大5倍,得6(x-1)+10(y+2)=25.8 (4)
用方程式(4)减去方程式(3) 得:19(y+2)=22.8 => y=-0.8
将y=-0.8代入方程式2(x-1)-3(y+2)=1,得 x=3.3
所以本组方程式的解是: x=3.3, y=-0.8