Steps to solve binary equations, solutions to binary equations

1. Elimination solution.

"Elimination" is the basic idea of solving binary linear equations. The so-called "elimination" is to reduce the number of unknowns, so that the multivariate equation is finally transformed into a one-dimensional multiple equation and then solve the unknowns. This method of solving the unknown number of equations one by one is called the elimination method.

Substitution of the elimination 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) Substitution method to solve the steps of 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 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 system of equations to test, whether the equation satisfies the left = right).

2. Addition, subtraction, and elimination method.

1) Concept: 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 unknown, so as to turn the binary equation into a one-dimensional equation, and finally obtain the solution of the system of equations, the method of solving the system of equations is called addition, subtraction and subtraction, referred to as addition and subtraction.

2) Steps to solve a system of binary equations by addition and subtraction.

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 (substitute into the original equation system to test, whether the equation satisfies the left = right).

A binary equation is an indefinite equation that has an infinite number of sets of solutions. When solving an equation, it is usually made to the left of the equation with an unknown, and to the right of the equation is an integer with another unknown, which is then brought into the solution.

General solution of binary linear equations:Elimination: Eliminate the number of unknowns in the equation system from more to less, and solve them one by one.

There are two ways to eliminate the element:

1. Substitute the elimination element.

Example: Solve the system of equations x+y=5 6x+13y=89 Solution: Bring in by x=5-y, get 6(5-y)+13y=89, and solve y=59 7

Bring y=59 7 to get x=5-59 7, i.e. x=-24 7 x=-24 7, y=59 7

This solution is the substitution method of elimination.

2. Addition and subtraction.

Example: Solve a system of equations x+y=9 x-y=5

Solution: + gives 2x=14, i.e. x=7

Bring x=7 into to get 7+y=9, and solve y=2

x=7，y=2

This solution is the method of addition and subtraction.

Solve the equation and write out the calculation process:

1. Substitute the value of the unknown into the original equation.

2. How much is the left side equal to, and whether it is equal to the right side.

3. Determine whether the value of the unknown is the solution of the equation.

For example: solution: x=23

x=5 test:

Substituting =5 into the equation yields:

Left ==23 = Right.

So, x=5 is the solution of the original equation.

Why didn't the landlord give an example question?

Binary equations only come in the form of systems of equations, and if they are not, there are infinite groups of solutions.

Example 1 has only one equation.

3x+2y=5

There are an infinite number of solutions to this equation, and you can give a random x value and a y value to make the equation true, as when x=1.

y=1, x=0.

y=, and many more, so I won't list them all here.

Example 2: A system of equations.

x+y=22x+3y=5

The general idea is to solve one of the equations first, for example, the first equation x+y=2 gets x=2-y

Substituting the second equation.

2(2-y)+3y=5

That is, 4-2y+3y=5

4+y=5 gives y=1

Then substitute into Equation 1.

x+1=2, get x=1

In the end, the solution of this system of equations is x=1y=1

The system of binary linear equations is transformed into a univariate linear equation. The method of elimination is "substitution", and this method of solving the system of equations is called substitution elimination method.

Solve the system of equations {5x+80=6y+20

1)｛4y=2x+80

2) Solution: obtained from (2).

y=1/2x+20

3) Substitute (3) into (1) to get:

5x+80=6(1/2x+20)+20

5x+80=3x+120+20

5x-3x=140-80

2x=60x=30

Substituting x=20 into (3) yields: y=1 2

y=15+20

y=35x=30

y=35

How to solve a system of binary equations!

When finding the solution of a binary linear equation, the usual practice is to use an unknown to represent another unknown, and then give a value to this unknown, and accordingly obtain the value of another unknown, so that a solution of the binary linear equation can be obtained.

1.Substitution of the elimination method.

An unknown number of an equation in a system of equations is expressed by an algebraic formula containing another unknown, substituted into another equation, an unknown number 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.Image method.

The binary linear equation system can also be used as an image method, that is, the corresponding binary linear equation is rewritten into the expression of the linear function and the image is drawn in the same coordinate system, and the coordinates of the intersection of the two straight lines are the solution of the binary linear equation system.

3.Commutation method.

When solving a math problem, a certain formula is treated as a whole and a variable is substituted for it, so that the problem is simplified, which is called the commutation method. The essence of the change element is to transform, so that non-standard problems are standardized and complex problems are simplified and become easy to deal with.

1. The solution method of unary equations: denominator to parenthesis to shift term to merge similar terms to the coefficient of transformation;

2. The solution of binary linear equations: basic idea: elimination;

3. Substitution method: use a letter instead of another one, y is equal to how many x, bring in the second equation, and solve the unary once;

4. Addition and subtraction: Transform the same unknown coefficient into a rubber slippery pattern, add and subtract to eliminate an unknown, and then solve one yuan once.

There are four solutions to a quadratic equation: the direct leveling method; Matching method; Formula method; Factorization. The basic idea of solving a one-dimensional quadratic equation is to reduce it into two unary one-dimensional equations by "descending".

1. Direct leveling method.

A one-dimensional quadratic equation of the shape of x Biling = p or Cong Huichan (nx+m) = p(p 0) can be solved by the direct open-level method. If the equation is formulated in the form x = p, then x = p is obtained. If the equation can be formed in the form of (nx+m) = p(p 0), then nx+m = p, and thus the root of the equation is obtained.

2. Matching method: use the matching method to solve the equation ax +bx+c=0 (a≠0), first move the constant c to the right side of the equation, turn the quadratic term coefficient into 1, add half of the square of the primary term coefficient on both sides of the equation, and the left side of the equation becomes a complete square.

3. Formula method: the unary quadratic equation is converted into a general form, and then the value of the discriminant formula = b -4ac is calculated, when b -4ac is 0, the value of the coefficients a, b, and c is substituted into the root formula to obtain the root of the equation.

4. Factorization method: deform the equation into zero on one side, decompose the quadratic trinomial formula on the other side into the form of the product of two primary factors, let the two primary factors equal to zero respectively, and obtain two unary equations, and the roots obtained by solving these two unary equations are the two roots of the original equation.

Establishment conditions. Three conditions must be met at the same time for the one-dimensional quadratic dust infiltration process to be established:

1. It is an integer equation, that is, both sides of the equal sign are integers, and if there is a denominator in the equation; And the unknown number is on the denominator, then this equation is a fractional equation, not a one-dimensional quadratic equation, if there is a root number in the equation, and the unknown number is in the root number, then this equation is not a one-element quadratic equation (it is an irrational equation).

2. Contains only one unknown.

3. The maximum number of unknown items is 2.