The method of solving a 2 element equation, how to solve a 2 element equation

If the large bottle is x bottle, then the small bottle is y bottle, then there are: 500 * x + 250 * y = (one ton = 1000kg = 1000000g).

x：y=2：5

Solving these two equations, the two equations yield: x=

Substituting x= into a formula, we get:

That is, 450y = 22500000

i.e. y=50,000 bottles.

Then x = bottle. If you don't ask for a problem like this, it's easier to solve it directly with a one-dimensional equation.

Let the large one be 2x bottles and the small one be 5x bottles.

500*2x+250*5x=225000002250x=22500000

x=10000

Then the large one: 2x = 20,000 bottles, and the small one: 5x = 50,000 bottles.

What about points? What about points?

How to solve the 2-element equation is as follows:

1. Substituting the elimination method: a certain unknown number of an equation in the system of equations is expressed by an algebraic formula containing another unknown, substituting into another equation, eliminating an unknown number, obtaining a one-dimensional one-dimensional equation, and finally obtaining the solution of the system of equations.

2. Addition, subtraction, and elimination method: When the coefficients of an unknown of two equations in the equation are equal or opposite to each other, the two sides of the two equations are added or subtracted to eliminate the unknown, so as to turn the binary equation into a one-dimensional equation, and finally obtain the solution of the system of equations.

Solution in detail:

First, substitute the elimination method

1. Select a binary equation with simple coefficients to deform and use an algebraic formula containing one unknown to represent another unknown;

2. Substitute the deformed equation into another equation, eliminate an unknown number, and obtain a unary 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);

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

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

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

6. The final test (substitute into the original equation system for testing, whether the equation satisfies the left = right).

Second, the method of addition and subtraction

1. Using the basic properties of the equation to convert the coefficient of an unknown number in the original equation system into the form of equal or opposite numbers;

2. Then use the basic properties of the equation to add or subtract the two equations after deformation, eliminate an unknown number, and obtain a unary equation (be sure to multiply the two 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 if the unknown coefficients are opposite, then use addition);

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

4. Substituting the value of the obtained unknown into any equation in the original system of equations to find the value of another unknown;

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

6. The final test is whether the result is correct (substituted into the original equation system for testing, whether the equation satisfies the left = right).

The method of solving a binary equation is as follows:

Substitution into the side resistance to the hidden elimination of mu filial piety method:

1) Concept: An unknown of an equation in a system of equations is expressed by an algebraic formula containing another unknown, substituted into another equation, an unknown is eliminated, a unary equation is obtained, and finally the solution of the system of equations is obtained. This method of solving a system of equations is called the substitution elimination method, or substitution method for short.

2) The steps of solving a system of binary linear equations by substitution method: select a deformation of a binary linear equation with simple coefficients, and use an algebraic formula containing one unknown to represent another 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 "{"; The final test (substituted into the original equation system to test, whether the equation satisfies the left = right).

Addition, subtraction, and subtraction:

When the coefficients of an unknown number of two equations in the equation are equal or opposite to each other, the two sides of the two equations are added or subtracted to eliminate the unused known number, so that the binary equation is transformed into a unary equation, and finally the solution of the system of equations is obtained, and the method of solving the system of equations is called the method of addition and subtraction, referred to as addition and subtraction.

The method of solving a binary equation is as follows:

Method 1: Substitution.

Represent one of the unknowns with the other. Substitute the resulting expression into another equation and eliminate one of the unknowns. Solve another unknown. Substituting the resulting unknowns into any one equation to find the other unknown.

Method 2: Elimination method.

Turns the coefficient of one of the two equations into an equal number. Subtract or add two equations to eliminate one of the unknowns. Solve another unknown. Substituting the resulting unknowns into any one equation to find the other unknown.

Method 3: Matrix method.

Write the system of binary equations in the form of a matrix. Find the inverse matrix of the coefficient matrix. Multiply the inverse matrix by the constant matrix to obtain the ungrasped rising knowledge matrix.

Method 4: Image Method.

Represent the two equations in the form of straight lines. Draw two straight lines in the coordinate system. Find the intersection of two straight lines, and the coordinates of that point are the solution of the equation.

An extension of the basic definition of binary linear equations:

An integer equation that contains two old unknowns, and the order of the terms containing the unknowns is 1, is called a binary equation. All binary linear equations can be reduced to the general expression of ax+by+c=0(a, b≠0) and the standard expression of ax+by=c(a, b≠0), otherwise they are not binary linear equations.

Use the deletion method to remove a variable first, such as synthesis.

3x+4y=12

4x+4y=13

Then subtract the two formulas to get x=1, and bring back either formula to get y=9 4

The 2-ary equation is solved by algebra, and an unknown quantity in the first equation is completely represented by another unknown quantity, and the expression is brought into the second equation, so that the 2-element equation is converted into a unary equation, and the result is solved to bring back the result of an equation, and the result is obtained!

As. x+2y=1

Represent an unknown quantity in the first equation with another unknown quantity, i.e., x=1-2y, and bring the expression into the second equation, i.e., 4(1-2y), and solve this unary equation to get y=4 19

Bring the result back to an equation that is: x=1-2*(4 19)=11 19, and the result is x=11 19

y=4/19

It's a system of binary equations. The main idea of solving a system of binary equations is to eliminate the element, that is, to eliminate an unknown number (one here refers to one). As for how to eliminate the element, one of the most common methods is to treat one of the unknowns as a known number and calculate another unknown, that is, to use one unknown to represent another unknown; Then substituting the algebraic formula into the equation can find these two unknowns.

There are other ways to eliminate the element, this needs to be summarized by yourself, if you type here, it's too troublesome, so I won't say much.