5y + z = -1 2x - y - z = 1 _Solving multivariate equations

Mathematics

语言：中文
Language:English

current location：Equations > Multivariate equations > Answer

Detailed information：
The input equation set is:

5

y

+

z

=

-1

(1)

2

x

-1

y

-1

z

=

1

(2)

0 =

0

(3)

Question solving process:

交After the exchange of equation (1) and equation (2)， the equation system becomes:

2

x

-1

y

-1

z

=

1

(1)

5

y

+

z

=

-1

(2)

0 =

0

(3)

Divide both sides of equation (2) by 5, get the equation：

y

+

1

5

z

=

-

1

5

(4)

, then add the two sides of equation (4) to both sides of equation (1), get the equation：

2

x

-

4

5

z

=

4

5

(1)

5

y

+

z

=

-1

(2)

0 =

0

(3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：

x

-

2

5

z

=

2

5

(1)

y

+

1

5

z

=

-

1

5

(2)

0 =

0

(3)

Therefore, the solution of the equation set is:

x =

2

5

+

2

5

z

y =

-

1

5

-

1

5

z

Convert the solution of the equation set to decimals:

x =

0.400000

+

2

5

z

y =

-0.200000

-

1

5

z

Where: z are arbitrary constants.
解方程组的详细方法请参阅：《多元一次方程组的解法》