聯立方程題

設蜘蛛有x隻, 蜻蜓有y隻, 蟬有z隻。

x + y + z = 18 --- ( 1 )

8x + 6y + 6z = 118

4x + 3y + 3z = 59 --- ( 2 )

( 0 )( x ) + 2y + z = 20

z = 20 - 2y --- ( 3 )

分別代( 3 )入( 1 )和(2 ),

x + y + 20 - 2y = 18

x - y = - 2

y = x + 2 --- ( 4 )

4x + 3y + 3 ( 20 - 2y ) = 59

4x + 3y + 60 - 6y = 59

4x - 3y = - 1 --- ( 5 )

代( 4 )入( 5 ),

4x - 3 ( x + 2 ) = - 1

4x - 3x - 6 = -1

x = 5

4 ( 5 ) - 3y = -1

3y = 21

y = 7

z = 20 - 2 ( 7 ) = 6

所以,

蜘蛛: 5隻



蜻蜓: 7隻



蟬: 6隻

設有蜘蛛 x 隻, 蜻蜓 y 隻, 蟬 z 隻
x + y + z = 18 -- (i)
8x + 6y + 6z = 118
ie. 4x + 3y + 3z = 59 -- (ii)
2y + z = 20
ie. z = 20 - 2y -- (iii)
4*(i) - (ii),
(4x+4y+4z) - (4x+3y+3z)= 72 - 59
y + z = 13 -- (iv)
sub (iii) into (iv), y + z = 13
y + 20-2y = 13
y = 7
in (iv), y + z = 13
z = 6
into (i), x + y + z = 18
x = 5
蜘蛛 5 隻, 蜻蜓 7 隻, 蟬 6 隻