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 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

Get from (1)

x=y+3③

③ Substitute into ② to get it.

3(y+3)-8y=4y= 1

Bring y= 1 into ③.

Get x=4.

Then: the solution of this binary linear equation system x=4y= 1.

Addition, subtraction and elimination method

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 value of the unknown quantity into any equation in the original equation to obtain the value of another unknown quantity;

⑤ Simultaneous two unknowns with "{"are the solutions of equations;

⑥ Finally, check whether the result is correct (substitute into the original equations and check whether the equations satisfy left = right).

For example: 5x+3y=9

10x+5y= 12

The first equation ① and the second equation ② are called.

①×2 to obtain ③

10x+6y= 18

③-②De: 10x+6y-( 10x+5y)= 18- 12y = 6。

Then substitute y=6 into ①, ② or ③.

Find the value solution of x: x=- 1.8.

y=6