The process of solving ternary equations is also described

The fourth one is very simple! Add the three equations and divide them by 2 to get: x+y+z=45

Then subtract the first, second, and third equations from the equation obtained above, respectively, to get:

z=18;x=12;y=15。

1）z=x+y

2x-3y+2z=5

x+2y-z=3

Solution: Substituting z=x+y into the remaining two formulas, then.

2x-3y+2（x+y）=5

x+2y-x-y=3

To simplify: 4x-y=5

y=3 substituting y=3 into 4x-y=5 yields: x=2 substituting x=2 and y=3 into z=x+y

z=52) x+2y+3z=11 a

x-y+4z=10 b

x+3y+2z=2 c

Solution: a-b 3y-z=1 d

c-a y-z=-9 e

d-e 2y=10 gives y=5

Substituting y=5 into 3y-z=1 gives z=14

Substituting y=5,z=14 into x+2y+3z=11 gives x=-413)x:y=1:5 3

y:z=5:6

x+y+2z=40

Solution: (5 3) x=y

z=(6/5)y

then z=(6 5)*(5 3)x z=2xx+(5 3)x+2x=40

x=60 7 y=100 7 z=120 7

1.Substituting one formula into three: y=3 and substituting one formula into two: x=2 solution: z=5

If you want to solve a ternary equation, you must have three different equations to solve it. Then use some two equations, eliminate one of them, become a binary system of equations, and then solve it. For example:

The sum of the three numbers of A and B is 26, A is 1 greater than B, and the sum of A and C is 18 greater than B.

Solution: Let A be x, B be y, and C be z.

Then: x+y+z=26

x-y=12x+z-y=18③

Transform the equation to x=1+y

Then replace the x in and with 1+y.

So. It becomes 1+y+y+z=26

That's 2y+z=25

This becomes 2(1+y)+z-y=18

That's z+y=16

Finally use the transformed - and it's done.

y=9 and then y=9

Substituting the transformed , so x=10

Finally, y=9, x=10 are substituted into the original ones.

That's 9 + 10 + z = 26

z=7, so x=10

y=9z=7

y=ax²+bx+c

When x=1 and y=3, the equation can be written as a+b+c=3 and denoted as an equation.

When x=2 and y=-1, the formula can be written as 4a+2b+c=-1 and denoted as the Zhongshan equation.

When x=3 and y=15, the equation can be written as 9a+3b+c=15 as an equation.

Equation 2-1 yields 3a+b=-4

Write as Equation 4

Equation 3-2 yields 5a+b=16

Write as Equation 5

Equation 5-4 yields 2a=20

then we get a=10

Bringing in Equation 4 gives us b = -34

Sell a and b respectively to the c=27 of equation 1

This yields a=10

b=-34c

The equation is y=10x-34x+27 from. x=5. y=107

1)x+2y+2z=3

3x+y-2z=7

2x+3y-2z=10. 4x+3y=10

3x+5y=13

3- *4, got.

y=2x=1

Substituting x=1y=2 into , gets.

z=-12)x-y=-1

2x+y+3z=5

x+y-z=1

*3, got. 5x+4y=8

4+, got.

x=4/9y=13/9

Will. x=4/9

y=13/9

Substitution, got.

z=8/93)x+y=8

y+z=-1

x+z=5-, get.

y-x=-6. y=1x=7 will.

y=1 substitution

Get. z=-2

4)x-y=2

z-x=3y+z=-1. y-x=4, the disadvantages are gained.

y=-3x=5

Will. x = 5 substitution. z=2

5)x-y-z=2

3x+5y+7z

4x-y+2z=26

5+, got.

4x+z=17

x+z=8-, get.

x=3z=5 will. x=3

z = 5 substitution into the shirt, nuclear divination cavity.

y=-4

(1)-(2) De:

x-y=5（4）

2) 3-(3) De:

5x+7y=76；（5）

5) (4) 7 get:

12x=111；

x=111/12=37/4;

Bring in (4) to:

y=17/4;

Bring in (1) to:

z=11/4;

So, the solution of the original system of equations is {x=37 4,y=17 4,z=11 4.}

- Find b

And then there are only two variables.

{x-2y=-9

1{y-z=3

2{2z+x

3 solution: obtained by formula 1.

x=-9+2y

Substitute x=---9+2y into formula 3 to get.

2z-9+2y=47

42 and 4 form a system of equations.

y-z=32z-9+2y=47