yanahv7的部落格

標題:

解聯二元一次方程

發問:

1. x=y 2x - y =27 2. x = -2y 4x + 2y = 24 3. x - y = 0 4x - 3y = -8 4. x + y = 0 -2x + 5y = 63 5. x - 5y = 0 2x - 7y = 18

最佳解答:

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1. { x = y ...[1] { 2x - y = 27 ...[2] 把 [1] 代入 [2], 2y - y = 27 y = 27 x = 27 { x = 27 { y = 27 2. { x = -2y ...[1] { 4x + 2y = 24 ...[2] 把 [1] 代入 [2], 4(-2y) + 2y = 24 -8y + 2y = 24 -6y = 24 y = -4 x = -2y = -2(-4) = 8 { x = 8 { y = -4 3. { x - y = 0 ...[1] { 4x - 3y = -8 ...[2] 從 [1] 可知 x = y ...[3] 把 [3] 代入 [2], 4y - 3y = -8 y = -8 x = -8 { x = -8 { y = -8 4. { x + y = 0 ...[1] { -2x + 5y = 63 ...[2] 從 [1] 可知 y = -x ...[3] 把 [3] 代入 [2], -2x + 5(-x) = 63 -2x - 5x = 63 -7x = 63 x = -9 y = -(-9) = 9 { x = -9 { y = 9 5. { x - 5y = 0 ...[1] { 2x - 7y = 18 ...[2] 從 [1] 可知 x = 5y ...[3] 把 [3] 代入 [2], 2(5y) - 7y = 18 10y - 7y = 18 3y = 18 y = 6 x = 5(6) = 30 { x = 30 { y = 6 2014-09-14 19:22:47 補充： 噢～不好意思～ 再一次謝謝 Leo 那麼有風度！ ??????????????? ～～Ｔｈａｎｋｓ！！！～～ ???????????????

其他解答:

1. { x = y ...[1] { 2x - y = 27 ...[2] 把 [1] 代入 [2], 2y - y = 27 y = 27 x = 27 { x = 27 { y = 27 2. { x = -2y ...[1] { 4x + 2y = 24 ...[2] 把 [1] 代入 [2], 4(-2y) + 2y = 24 -8y + 2y = 24 -6y = 24 y = -4 x = -2y = -2(-4) = 8 { x = 8 { y = -4 3. { x - y = 0 ...[1] { 4x - 3y = -8 ...[2] 從 [1] 可知 x = y ...[3] 把 [3] 代入 [2], 4y - 3y = -8 y = -8 x = -8 { x = -8 { y = -8 4. { x + y = 0 ...[1] { -2x + 5y = 63 ...[2] 從 [1] 可知 y = -x ...[3] 把 [3] 代入 [2], -2x + 5(-x) = 63 -2x - 5x = 63 -7x = 63 x = -9 y = -(-9) = 9 { x = -9 { y = 9 5. { x - 5y = 0 ...[1] { 2x - 7y = 18 ...[2] 從 [1] 可知 x = 5y ...[3] 把 [3] 代入 [2], 2(5y) - 7y = 18 10y - 7y = 18 3y = 18 y = 6 x = 5(6) = 30 { x = 30 { y = 6|||||又迟咗.搬到意見柵 1. x=y 2x - y =27 put x=y into 2x - y =27 2x - x =27 x =27 y=27 2. x = -2y 4x + 2y = 24 put x= -2yinto 4x + 2y = 24 4(-2y) + 2y = 24 y=-4 x = -2(-4)=8 2014-09-14 19:19:09 補充： 3. x - y = 0 4x - 3y = -8 From x - y = 0, x = y put x=y into 4x - 3y = -8 4x - 3x = -8 x = -8 y= -8 4. x + y = 0 -2x + 5y = 63 From x + y = 0, x = -y put x=-y into -2x + 5y = 63 -2(-y) + 5y = 63 7y= 63 y=9 x=-9 2014-09-14 19:19:14 補充： 5. x - 5y = 0 2x - 7y = 18 From x - 5y = 0, x =5y put x =5y into 2x - 7y = 18 2(5y) - 7y = 18 3y = 18 y = 6 x =5(6)=30