X-y=8 1 formula
3x-4y= 17 2 formula
Set 8+ y=x in formula 1 to formula 3.
Substitute Equation 3 into Equation 2, and include one unknown with another unknown.
Question 2: What is the formula for solving binary linear equations? 1) substitution elimination method
The concept of (1): the unknown number of one equation in the equation group is expressed by an algebraic expression containing another unknown number, then it is substituted into another equation, and an unknown number is eliminated to obtain a linear equation with one variable, and finally the solution of the equation group is obtained. This method of solving equations is called substitution elimination method, or substitution method for short.
(2) The step of solving binary linear equations by substitution method.
① A binary linear equation with simple coefficients is selected for deformation, and an algebraic expression containing an unknown number is used to represent another unknown number;
(2) Substitute the deformed equation into another equation, eliminate an unknown number, and get a linear equation (when substituting, be careful not to substitute into the original equation, only substitute into another equation without deformation, so as to achieve the purpose of elimination);
③ Solve this one-dimensional linear equation and get the unknown value;
(4) Substituting the obtained unknown values into the deformation equation in (1),
Find the value of another unknown;
⑤ Simultaneous two unknowns with "{"are the solutions of equations;
⑥ Final test (substitute the original equation to test whether the equation satisfies left = right).
Example:
{x-y=3 ①
{3x-8y=4②
X=y+3③ Starting from ①.
③ Substitute into ② to get it.
3(y+3)-8y=4
y= 1
Bring y= 1 into ③.
Get x=4.
Then: the solution of this binary linear system of equations
2) Addition, subtraction and elimination methods
The concept of (1): When the coefficients of the unknowns of two equations in an equation are equal or opposite, the unknowns are eliminated by adding or subtracting the two sides of the two equations, so that the binary linear equation is transformed into a univariate linear equation, and finally the solution of the equation is obtained. This method of solving equations is called addition, subtraction and elimination, or addition and subtraction for short.
(2) Add and subtract steps to solve binary linear equations.
① Using the basic properties of the equation, the coefficient of an unknown quantity in the original equation is transformed into an equal or opposite number;
(2) Using the basic properties of the equation, add or subtract two deformation equations to eliminate an unknown number, and get a linear equation (both sides of the equation must be multiplied by the same number, and it is forbidden to multiply only one side. If the unknown coefficient is equal, it will be subtracted, and if the unknown coefficient is opposite, it will be added);
③ Solve this one-dimensional linear equation and get the unknown value;
(4) substituting the obtained unknown value into any equation in the original equation set,
Find the value of another unknown;
⑤ Simultaneous two unknowns plus "{"is the solution of the equations.
;
⑥ Finally, check whether the result is correct (substitute into the original equations and check whether the equations satisfy left = right).
For example:
The first equation ① and the second equation ② are called.
①×2 to obtain ③
10x+6y= 18
③-② Obtain:
10x+6y-( 10x+5y)= 18- 12
3) Alternative methods
When solving a mathematical problem, we regard a formula as a whole and replace it with a variable, thus simplifying the problem. This is called substitution. The essence of substitution is transformation, the key is to construct elements and set elements, and the theoretical basis is equivalent substitution. The purpose is to change the research object, move the problem to the knowledge background of the new object, standardize non-standard problems, simplify complex problems and become easy to deal with.
Substitution method is also called auxiliary element method and variable substitution method. By introducing new variables, scattered conditions can be linked, implicit conditions can be revealed, or conditions can be linked with conclusions. Or turn it into a familiar form to simplify complicated calculation and derivation.
It can transform high order into low order, fraction into algebraic expression, irrational expression into rational expression, transcendental expression into algebraic expression, and has a wide range of applications in the study of equations, inequalities, functions, sequences, triangles and other issues.
take for example
(x+y)/2-(x-y)/3=6①
3(x+y)=4(x-y)②
Solution: let x+y be a and X-Y be b.
So, the original equation becomes
a/2-b/3=6③
3a-4b=0 ④
Solution:
a=24
b= 18
Therefore:
x+y=24
x-y= 18
The solution of the equation is:
x= 2 1
y= 3 ....& gt& gt
Question 3: What is the root formula of binary linear equation? One-dimensional quadratic equation: For the equation: AX2+BX+C = 0:
B2-4ac is called the discriminant of roots. ① the formula for finding the root is x.
When △ > 0, the equation has two unequal real roots; When △ = 0, the equation has two equal real roots;
When △ < 0, the equation has no real root. Note: When △≥0, the equation has real roots.
② If the equation has two real roots x 1 and x2, and the quadratic trinomial AX2+BX+C can be decomposed into a (X-X 1) (X-X2). ③ The quadratic equation with roots A and B is X2-(A+B) X+AB = 0.
Question 4: How to solve the binary linear equation? To understand the concept of binary linear equation, we should pay attention to the following points:
(1) Whether the algebraic expressions on both sides of the equal sign are algebraic expressions;
(2) In the equation, "yuan" refers to an unknown number, and "binary" refers to an equation containing two unknowns;
(3) The degree of the unknown term is 1, which actually means that the degree of the highest term in the equation is 1, which can be compared with the degree of polynomial. Must not be understood as two unknowns, the number of times is 1.
(2) The solution of binary linear equation
A set of unknown values that make both sides of a binary linear equation equal is called the solution of a binary linear equation.
To understand the solution of binary linear equation, we should pay attention to the following points:
Generally speaking, a binary linear equation has countless solutions, and each solution refers to a pair of values, not a single unknown value;
(2) A solution of a binary linear equation refers to a pair of unknowns whose left and right sides are equal; On the other hand, if a set of values can make the left and right sides of a binary linear equation equal, then this set of values is the solution of the equation;
(3) When solving a binary linear equation, the usual practice is to use one unknown to represent another unknown, and then give this unknown a value, and correspondingly get the value of another unknown, so that a solution of the binary linear equation can be obtained.
Question 5: Is there any trick to learn binary linear equation?
(1) Concept: An equation with algebraic expressions on both sides and two unknowns, with the unknown degree of 1, is called a binary linear equation. [1] The value of the unknown that makes the left and right sides of the equation equal is called the solution of the equation.
Can you distinguish these equations? 5x+3y=75 (binary linear equation); 3x+ 1=8x (linear equation of one variable); 2y+y=2 (linear equation of one variable); 2x-y=9 (binary linear equation).
When understanding the concept of binary linear equation, we should pay attention to the following points:
(1) Whether the algebraic expressions on both sides of the equal sign are algebraic expressions;
(2) In the equation, "yuan" refers to an unknown number, and "binary" refers to an equation containing two unknowns;
(3) The degree of the unknown term is 1, which actually means that the degree of the highest term in the equation is 1, which can be compared with the degree of polynomial. Must not be understood as two unknowns, the number of times is 1.
(2) The solution of binary linear equation
A set of unknown values that make both sides of a binary linear equation equal is called the solution of a binary linear equation.
To understand the solution of binary linear equation, we should pay attention to the following points:
Generally speaking, a binary linear equation has countless solutions, and each solution refers to a pair of values, not a single unknown value;
(2) A solution of a binary linear equation refers to a pair of unknowns whose left and right sides are equal; On the other hand, if a set of values can make the left and right sides of a binary linear equation equal, then this set of values is the solution of the equation;
(3) When solving a binary linear equation, the usual practice is to use one unknown to represent another unknown, and then give this unknown a value, and correspondingly get the value of another unknown, so that a solution of the binary linear equation can be obtained.
system of equations
(1) Binary linear equations: An equation group consisting of two binary linear equations is called binary linear equations. [2]
(2) Solution of binary linear equations: The common solution of two equations in binary linear equations is called the solution of binary linear equations.
Attention should be paid to the understanding of binary linear equations:
① In each equation of the equations, the same letter must represent the same quantity, otherwise the two equations cannot be merged.
(2) How to test whether a set of numerical values is the solution of binary linear equations? The common methods are: substituting this set of values into each equation of the equation group, and only when this set of values satisfies all equations can it be said that this set of values is the solution of this equation group; Otherwise, if this set of values does not satisfy any equation, it is not the solution of this equation group.
elimination by substitution
The concept of (1): The unknown number of one equation in the equation set is expressed by an algebraic expression containing another unknown number, which is substituted into another equation, and an unknown number is eliminated to obtain a linear equation with one variable, and finally the solution of the equation set is obtained. This method of solving equations is called substitution elimination method, or substitution method for short.
(2) The step of solving binary linear equations by substitution method.
① A binary linear equation with simple coefficients is selected for deformation, and an algebraic expression containing an unknown number is used to represent another unknown number;
(2) Substitute the deformed equation into another equation, eliminate an unknown number, and get a linear equation (when substituting, be careful not to substitute into the original equation, only substitute into another equation without deformation, so as to achieve the purpose of elimination);
③ Solve this one-dimensional linear equation and get the unknown value;
(4) Substituting the obtained unknown quantity into the deformation equation in (1) to obtain the value of another unknown quantity;
⑤ Simultaneous two unknowns with "{"are the solutions of equations;
⑥ Final test (substitute the original equation to test whether the equation satisfies left = right).
Example:
{x-y=3 ①
{3x-8y=4②
X=y+3③ Starting from ①.
③ Substitute into ② to get it.
3(y+3)-8y=4
y= 1
Bring y= 1 into ③.
Get x=4.
Then: the solution of this binary linear system of equations
{x=4
{y= 1
Addition, subtraction and elimination method
(1) Concept: When the coefficients of an unknown number of two equations in an equation are equal or opposite, the unknown number is eliminated by adding or subtracting the two sides of the two equations, thus transforming a binary linear equation into a univariate linear equation and finally getting the solution of the equation. This method of solving equations is called addition, subtraction and elimination, or addition and subtraction for short.
(2) Add and subtract steps to solve binary linear equations.
① Using the basic properties of the equation, the coefficient of an unknown quantity in the original equation is transformed into an equal or opposite number;
(2) Using the basic properties of the equation, add or subtract two deformation equations to eliminate an unknown number, and get a linear equation (I >；); & gt