初二二元方程组题目一道,在线等.3/x+y + 1/x-y = 8 { 2/x+y -1/x-y =7 要过程
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![初二二元方程组题目一道,在线等.3/x+y + 1/x-y = 8 { 2/x+y -1/x-y =7 要过程](/uploads/image/z/4519905-33-5.jpg?t=%E5%88%9D%E4%BA%8C%E4%BA%8C%E5%85%83%E6%96%B9%E7%A8%8B%E7%BB%84%E9%A2%98%E7%9B%AE%E4%B8%80%E9%81%93%2C%E5%9C%A8%E7%BA%BF%E7%AD%89.3%2Fx%2By+++%2B++1%2Fx-y++%3D++8++++++++%EF%BD%9B++++++2%2Fx%2By++++-1%2Fx-y+++++%3D7+%E8%A6%81%E8%BF%87%E7%A8%8B)
初二二元方程组题目一道,在线等.3/x+y + 1/x-y = 8 { 2/x+y -1/x-y =7 要过程
初二二元方程组题目一道,在线等.
3/x+y + 1/x-y = 8
{
2/x+y -1/x-y =7
要过程
初二二元方程组题目一道,在线等.3/x+y + 1/x-y = 8 { 2/x+y -1/x-y =7 要过程
3/x+y + 1/x-y = 8 (1)
2/x+y -1/x-y =7 (2)
(1)+(2)得 5/x+y=15 x+y=1/3 (3)
把(3)代入方程(1)得 3÷(1/3)+1/x-y=8 9+1/x-y=8 x-y=-1 (4)
(3)+(4)得 2x=-2/3 x=-1/3
(3)-(4)得 2y=4/3 y=2/3
即 x=-1/3
y=2/3
希望你明白
设a=1/(x+y), b=1/(x-y)
原方程组可化为3a+b=8 2a-b=7
容易解得a=3 b=-1
所以x+y=1/3 x-y=-1
也容易解得x=-1/3 y=2/3
方程1 + 方程2 得 5/x+y =15, 即 x+y=1/3
2*方程1 - 3*方程2 得 5/x-y =-5, 即 x-y=-1
由此得出 x=-1/3, y=2/3
1
令m=1/(x+y),n=1/(x-y)得:3m+n=8……(1),2m-n=7……(2)
(1)+(2)得5m=15,m=3代入(1)得n=-1
1/(x+y)=3,1/(x-y)=-1
化简得x+y=1/3, x-y=-1解得:x=-1/3,y=2/3