Question

若关于X、Y的方程组2X+3Y=4K+9,X-2Y=6K+7的解X、Y的值之和为2004,试求K的值

Answer 1

2X+3Y=4K+9 (1)

X-2Y=6K+7 (2)

(1)-(2)x2

3Y+4Y=4K+9-12K-14

7Y=-8K-5

Y=-(8K+5)/7

(1)x2+(2)x3

4X+3X=8K+18+18K+21

7X=26K+29

X=(26K+29)/7

X+Y=2004

(26K+29)/7-(8K+5)/7=2004

26K+29-8K-5=2004x7

18K=14004

K=/18

K=778