Math 3 Element Equation Problem Math experts, please enter

Question 1: i=1, x=3, y=5 (Method: Add or subtract different equations, remove the third unknown to make it a binary system of equations, and then add and subtract to subtract the second unknown).

Question 2: The method is the same as above, because the oral arithmetic is a bit difficult, as your practice can be completed by yourself.

No, play me, there are no questions, and what do people do.

There is no fixed way to solve a ternary equation, unlike binary equations, which have a fixed formula, and to solve a ternary equation, you must first find a solution to the equation by observation, and then decompose the factor.

1.First of all, let's talk about the first two formulas to do subtraction operations. x-i=2.It can be calculated by adding it to the third equation. x=3...So i=1.y=5..

2.Same approach. The second equation is transformed first.

Multiply both sides of the equation by 3 at the same time to get 6x+9y+3z=27....Plus the third formula. 11x+10z=35....

Then we can calculate x=5.z=-2...y=1/3

1.Substituting y=8-x into the second equation gives 8-x+i=6, and merging the above equation with the third equation to obtain i=1, x=3, y=5;

2.Multiply Eq. 2 by 3: 6x+9y+3z=27, add it to Eq. 3 (left + left, right + right) to get 11x+10z=35, and then calculate it with Eq. 1 (preferably proportionally expanded) to get x=5, z=-2, y=1 3

1.Subtract the first two equations to give x-i=2, and combine with the third equation to solve x=3, i=1

Bringing in the first equation gives y=5

2.Multiply the second equation by 3 to get 6x+9y+3z=27, combine with the third equation to solve, 11x+10z=35, combine with the first equation, solve, x=5, z=-2, bring in the second equation, get y=1 3 complete!

1.Equation Isn't that right?

The total distance is kilometers, x 3+y 4+z 5=51 60 x+y+z=

z/3+y/4+x/4= ③

, get: x+z)*7 12+y 2=

From , we get: x+z=

Substitution, get:

y 12 = y = substitution , get:

x+z=x+z=

, gets: 1 12*(z-x)=

z-x=+ , get:

2z=z=- , get:

2x=x=A: From A to B, kilometers uphill, kilometers on flat roads, kilometers on downhill roads

2x-3z=1 ②

3x-y+2z=4 ③

2+, got:

7x+3z=8………

, gets: 9x=9

x=1 is substituted to get :

2-3z=1

3z=1z=1/3

From , get: 1+2y-1 3=0

2y=-2/3

y=-1/3

The solution is: x=1

y=-1/3

z=1 3 The main way to solve multivariate equations is to eliminate elements.

Commonly used are addition, subtraction, and substitution.

1. The first system of equations should be:

x/3+y/4+z/5=51/60 ①x+y+z= ②

z/3+y/4+x/5= ③

Equation by denominator: 20x 15y 12z 51 Equation by denominator: 12x 15y 20z: 8z 8x

z－x＝z＝x＋ ⑥

Substituting z x into get:

20x＋15y＋12x＋

32x＋15y＝ ⑦

Substituting z x into get:

x＋y＋x＋

y＝3－2x ⑧

Then substitute y 3 2x into :

32x＋45－30x＝

2x x substitute x into :z

Substituting x into 8 gives :y

2. Note that there are only two unknowns x and z in the equation, so we can consider subtracting y from , to get a relation to x and z

2 gets: 7x 3z 8

, gets: 9x=9

x 1 put x 1 into it:

7＋3z＝8

z 1 3 x 1, z 1 3 substitution:

1＋2y－1/3＝0

Got y 1 3

In this way of solving the equation, if you are a novice, you first digitize the number before each unknown number as an integer, such as one-third x, then multiply each side of the equal sign by three. Then take two of them, such as 1 and 2 in your first questionFirst, the 1 is an integer, the least common divisor is 60, so both sides are multiplied by 60, and so on 1 becomes 20x+15y+12z=51, and then find a way to subtract or add 1,2 to get rid of an unknown number.

Multiply the two sides of Eq. 2 by 20, and Eq. 2 becomes 20x+20y+20z=640Subtract the two formulas, subtract the formula 1 from the formula, and get 5y+8z=589, and then express one unknown in this formula with another unknown. For example, y is expressed in z, so that the expression is brought into the 2 and 3 formulas, and then it becomes a 2 yuan equation, I believe you can solve it.

This kind of problem usually makes up all the numbers, otherwise it is very troublesome to solve, and I don't need to see if your equation is right or wrong. I just said how to solve it... Just practice more.

The second equation should not be x+y+z=

x/3+y/4+z/5=51/60 ①x+y+z= ②

z/3+y/4+x/5= ③

③ z-x=

15* -5z-3x = so.

x=y=z=

System of Equations 1

Three equations are tentatively named equations at a time

Subtract Equation 2 from Equation 1 to get x-z=2a-2b (this equation is tentatively called Equation 4).

Now add Equation 3 to Equation 4 to get 2x=2a-2b-2c

then, x=a-b-c

Substituting the value of x into Equation 1 gives a-b-c+y=2a

Then there is: y=a+b+c

Substituting the value of x into Equation 3 gives a-b-c+z=2c

Then there is: y=b+3c-a

The same three equations in Equation 2 are tentatively named equations at one time

Then Equation 3 yields y=3x+z (Equation 4).

Substituting Equation 4 into Equation 1 gives 2x-6x-2z-3z=a, i.e., -4x-5z=a, then (Equation 5).

Substituting Equation 4 into Equation 2 gives x+12x+4z+2z=7a, i.e., 13x+6z=7a (Equation 6).

Multiply the left and right sides of Equation 5 by 6 at the same time, then -24x-30z=6a (Equation 7).

Multiply the left and right sides of Equation 6 by 5 at the same time, and it is 65x+30z=35a (Equation 8).

Now add the left and right sides of equations 7 and 8 respectively to get 41x=41a

So x=a substituting the value of x into equation 7 gives -24a-30z=6a, i.e., -30z=30a

So z=-a

Substituting the values of x and z into Equation 4 gives y=3a-a

So y=2a

The system of ternary equations can be solved by substitution.

The same is true for the word questions. The column equations are then solved synchronously.

Stupid: If you don't draw a picture, you can answer them blindly?

1、x-y+4z=5

2、 y-z+4x=-1

3、z-x-4y=4

Formula 1 + formula 2 gives x+3z=4 formula 2 * 4+3 formula gives x-3z=0, that is, z=5x substituting formula 4 to get x=1 5

Substituting x=1 5 into 5 gives z=1

Substituting x=1 5 and z=1 into any of the formulas gives y=-4 5, so x=1 5 y=-4 5 z=1

x-y+4z=5 ①

y-z+4x=-1 ②

z-x-4y=4 ③

③=>x-y=1 ④

Substituting into , we get z=1 and substituting z into , and we get y+4x=0

x+4y=-3 ⑥

y=-4x is substituted into .

Get x-16x=-3 x=1 5

y=-4/5

The three formulas are added together.

4x-4y+4z=8

Divide by four x-y + z = 2

x-y+4z=5

3z=3z=1 by.

y-1+4x=-1

x-y+1=2

Get y+4x=0

x-y=1, so x=1 5, y=-4 5

According to the last formula: z=4+4y+x

Bring in the second formula: 3x-3-3y=0 Introduce x=y+1 and bring in the first formula: y+1-y+4(4+4y+y-1)=5 and introduce y=-4 5

x=1/5z=1

Result: z = 2x+3y-11

Substituting respectively, 3 gets:

2x+y-5(2x+3y-11) = 8

2x+7y+ 2x+3y-11 = 19-》8x+14y=47 ④

y = 30

y = 3 substitution to get x = 5 8

z = -3/4

- Get 2y+4z=3

8y-4z=27

Get y=3y=3 and substitute z=-3 4

y=3,z=-3 4 substituted by x=5 4

x=5/4y=3,z=-3/4

Pikay Crack -=-1-<3>

x+y-x-z=-1-3

y-z=-4

Use -=2-<-4 > again

Remove the parentheses, y+z-y+z=2+4

2z=6z=3

Substituting z=3 into the equation and y+3=2

y=-1 and then bring y=-1 into , x+"Dust closed -1>=-1x-1=-1

x=0 and that's fine.

In this way, Sun Zheng was established.

2-1, got.

z-x=1 4

4 and this fierce 3 composition equation Sen Liang Bridge Group slag suspicion, get.

z-x=1x+z=3x=0

y=-1z=3

It's easiest to do it yourself.

x=0y=-1z=3

An example of a ternary linear equation for the solution of the vertical group of the Lingling.

In the equation 5x 2y z 3, if x 1, y 2, then z

The monomial is known to be 8a3x y z

b12cx y z and 2a4b2x y 3zc6, then x y z

3 Solve a system of equations.

x＋y－z＝11,y＋z－x＝5,z＋x－y＝1

then x y z

4 The algebraic formula ax2 bx c is known, and when x 1, its value is 4; When x 1, its value is 8; When x 2, its value is 25; When x 3, its value is

5 x 3y 2z 0

3x－3y－4z＝0

then x y z

6. Solve the system of equations.

x＋y－z＝11

y z feast big x 5

z x y 1 To make the operation easy, the elimination method should be chosen (

a. Eliminate x first

b. Eliminate y first

c. Eliminate z first

d. None of the above statements are correct.

7 System of equations x y 1

x＋z＝0y＋z＝1

The solution is (y 1z 0bx 1

y＝0z＝－1cx＝0

y＝1z＝－1dx＝－1

y＝0z＝1

8 If x 2y 3z 10, 4x 3y 2z 15, then the value of x y z is (

a、2b、3

c、4d、5

9 If the system of equations 4x 3y 1

ax＋（a－1）y＝3

If the solution x is equal to y, then the value of a is equal to (

a、4b、10

c、11d、12

10 Knowing x 8y 2(4y 1)2 3 8z 3x 0, find the value of x y z.

11 Solving systems of equations.

x＋y－z＝6

x－3y＋2z＝1

3x＋2y－z＝4

12 If a couple is six times the age of their children, who were 10 times the age of their children two years ago, and who are three times the age of their children six years later, and who are three times the age of their children six years later?

3y=2zx+y+z=6

2x+y-z=2

x+2y-z=5

x-y+2z=-7

y＋z＝5x＋z＝6

It should be 2x-y+z=6.

Multiply by 5 and add to give 10x-2y=30

Coupled with 1, it is a system of binary equations.

*2 gets: 6y=30, y=5

Bring it in and you will solve x=4

Bringing in both x and y solves z=3

So: x=4 y=5 z=3

If it is not 2x-y+z=6

You ask again

Substituting the formula from z=6 gives 3y-30=0, so y=10 brings in the formula x = 8

So x = 8

y = 10

z = 6