The 3 element equation and the 2 element equation are up

1. When x=-, what is y=20 x?

2. The speed of the ship is x, and the water speed is y

then x+y=36 3 x-y=24 3

Solution, the speed of the ship is 10,000 kilometre, and the speed of the water is 2,000 kilometre.

3. Set up x eight-person cars and Y four-person cars.

8x+4y=36

1) A solution can be given.

x=1 y=7

x=2 y=5

x=3 y=3

x=4 y=1

2) Due to the small number of schemes, the cost of each scheme can be directly calculated.

It can be seen that 4 eight-person cars, 1 four-person car is the most economical.

1. When x=-??, y=20

2. When the speed of the water flow is (10) thousand miles, the speed of the ship in still water is (2) thousand miles.

Plan 1: 1 eight-seater, 7 four-seater, rent 1,700 yuan;

Plan 2: 2 eight-seaters, 5 four-seaters, rent 1,600 yuan;

Plan 3: 3 eight-seater cars, 3 four-seater cars, rent 1,500 yuan;

Plan 4: 4 eight-seater cars and 1 four-seater car, the rent is 1400 yuan.

It can be seen that the plan with the least rental cost is 4 eight-seaters and 1 four-seater, and the rent is 1,400 yuan.

1、－2＝a+b+c

20=a-b+c

9a 4+3b 2+c=a 9+b 3+c gives a 66 7 b -11 c 129 72, water velocity (36-24) 2 3=2 thousand miles.

Speed (36+24) 2 3=10 km/h.

2) An eight-seater car seats 8 people, and the cost is less than 2 4-seater cars, so the scheme should use as many eight-seater cars as possible, that is, 4 8 8 8 8

Question 1: a+b+c=-2,a-b+c=20,6 4a+3 2b=1 9a+1 3b

It can be solved a=6, b=-11, c=3

Problem 2: Let the water flow rate be x and the still water velocity be y

36=3(x+y),24=3(y-x)

It can be solved with x=2 and y=10

Question 3: There are x cars for 8 people and y cars for 4 people.

1)8x+4y=36 x=1,y=7; x=2,y=5; x=3,y=3;

2) Compare the size of 300x+200y to get x=4, y=1 is the best solution.

1. y=ax^2+bx+c

Solve the ternary equation { a+b+c=-2

a-b+c=20

4 6a+3 2b+c=1 9a+1 3b+c, which gives {a=b=c=

When x=3 2 and x=1 3, the value of y is equal, indicating that the axis of symmetry is x=11 12

The system of ternary equations, referred to as the ternary equation buried group or three-solution problem, is an important application problem in mathematics. It refers to an integral equation consisting of 3 unknowns x1, x2, y1, and y2 that satisfies :

a=b+ca, b are any two positive integers;

c is a constant term.

The methods for solving ternary equations mainly include direct method, matching method, factorization method and formula method. Among them, the formula method is a common method to solve binary one-dimensional algebraic inequalities, and it is also one of the basic solutions of ternary one-dimensional equations. Note: A quadratic equation can also be seen as a system of ternary equations.

One. Definition. Let an integer equation with two unknowns (x1, x2) be called a binary sine function relationship, which is represented by letters:

The integer of the form (x2, y1)· x3, y2) is called binary binomial relations, which is represented by letters: Shape like (x2, y1)· x3, y2) is called a binary cubic function relation, and the difference between a univariate quadratic and a quadratic function relation is that the former has only one unknown number and the latter has three unknowns.

Two. Basic nature.

1.The graph of a quadratic function is like a straight line.

2.The image of the quadratic function passes through the origin.

3.The quadratic function has the greatest value of eggplant early on the closed interval.

A ternary equation is an equation that contains three unknowns and the number of terms of the unknowns is 1, that is, a one-dimensional equation with three unknowns, and its general form is ax+by+cz=d. The system of equations composed of multiple unary equations and containing three unknowns is called a ternary equation, and its solution method is generally to dig the key and use the idea of eliminating the element to make the ternary become binary and judge the remainder, and then change the unary.

The value that fits each pair of unknowns of a ternary equation is called a solution of the ternary equation. For any one ternary equation, taking any two of the two unknowns will give the value of the other unknown corresponding to it. Therefore, any ternary equation has an infinite number of solutions, and the set of these solutions is called the solution set of this ternary equation.

Definition: A system of equations consisting of multiple unary linear equations containing three unknowns is called a system of ternary linear equations. Note:

Every equation does not necessarily contain three unknowns, but the system of equations as a whole contains three unknowns. Solution: The basic idea of solving the system of ternary equations is still elimination, and its basic method is to substitute the elimination method and the addition and subtraction elimination.

Steps: Using substitution or addition and subtraction, an unknown number is eliminated to obtain a binary system of equations; Solve this binary one-time square to destroy the companion group, and obtain the values of two unknowns; Substituting the values of these two unknowns into an equation containing three unknowns in the original equation to find the value of the third unknown, and writing the values of these three unknowns together in curly braces is the solution of the system of ternary equations.

The biggest difference between them is that the number of unknowns is the same. Binary Linear Equations.

There are two unknowns; Ternary Linear Equations.

There are three unknowns.

Binary Linear Equation: If an equation contains two unknowns, and the exponent of the unknown is 1, then the integer equation is called a binary equation with infinite solutions. The general form of a binary linear equation: ax+by+c=0 (a, b is not 0).

Ternary Equation: If an equation contains three unknowns, and the exponent of the unknown hail is 1, then the integer equation is called a ternary equation with infinite solutions. The general form of a ternary equation:

ax+by+cz+d=0 (a, b, c are not 0).

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

Obtained from (1).

x=(3/2)y

Obtained from (2).

z=(4 5)y, substituting the upper Qiaoye collapse into (3).

3 2) y+y+(4 filial piety 5)y=66,get.

y=20, so.

x=(3 spine oranges2)*20=30,z=(4 5)*20=16

Unary Equation:

Solving equations is based on these three properties of the equation.

The value of an unknown that equalizes the left and right sides of the equation is called the solution of the equation.

General solution. Denominator: multiply by the least common multiple of each denominator on both sides of the equation (the term without the denominator is also multiplied);

Basis: Nature of Equation 2

Remove parentheses: Generally, first go to the parentheses, then the middle brackets, and finally the curly braces, which can be assigned according to the multiplication (remember that if there is a minus sign or a division sign outside the parentheses, you must change the sign).

Basis: Multiplicative distributive law.

Shift: Move all terms with unknowns in the equation to one side of the equation (generally move the terms with unknowns to the left of the equation and move the constant terms to the right).

Basis: Nature of the equation 1

Merge similar terms: Equations are formed in the form ax=b(a≠0);

Basis: Multiplicative distributive (inverse multiplicative distributive property).

The coefficient is reduced to 1: the coefficient a of the unknown number is divided by both sides of the equation to obtain the solution of the equation x=b a

Basis: Nature of Equation 2

Binary Linear Equations.

First, the steps of substituting the method to solve a system of binary linear equations.

A binary linear equation with simple coefficients is selected to deform and another unknown is represented by an algebraic formula containing one unknown.

Substitute the deformed equation into another equation, eliminate an unknown number, and obtain a unary one-dimensional equation (when substituting, it should be noted that the original equation cannot be substituted, but can only be substituted into another equation without deformation, so as to achieve the purpose of elimination.)

Solve this unary equation and find the value of the unknown;

Substituting the value of the obtained unknown into the deformed equation to find the value of another unknown;

The value of two unknowns is the solution of the system of equations by "{";

Finally, check whether the results obtained are correct (substituted into the original equation system for testing, whether the equation satisfies the left = right).

Second, the steps of addition and subtraction to solve a system of binary linear equations.

Using the basic properties of the equation, the coefficient of an unknown number in the original equation system is reduced to the form of equal or opposite numbers;

Then use the basic properties of the equation to add or subtract the two deformed equations, eliminate an unknown number, and obtain a unary equation (be sure to multiply both sides of the equation by the same number, do not multiply only one side, and then use subtraction if the unknown coefficients are equal, and add if the unknown coefficients are opposite to each other);

Solve this unary equation and find the value of the unknown;

Substituting the value of the obtained unknown into any one of the original equations to find the value of another unknown;

The value of two unknowns is the solution of the system of equations by "{";

Finally, check whether the results obtained are correct (substituted into the original equation system for testing, whether the equation satisfies the left = right).

Ternary Linear Equations.

Their main solution method is the addition and subtraction elimination method and the substitution elimination method, usually using the addition and subtraction elimination method, if the system of equations is difficult to solve, the substitution elimination method is used, which varies from problem to problem (similar to the solution method of binary equations).