(a) fill in the blanks (2 points for each question, ***26 points):

1. It is known that the binary linear equation = 0, and X is expressed by an algebraic expression containing Y, then X = _ _ _ _ _ _ _ _ _ _ _ _；;

When y =-2 and X = _ _ _ _ _ It is suggested to take y as a known number to solve x, and the answer is X =；; x=。

2.( 1), (2) and (3), _ _ _ is the solution of equation x-3y = 9, _ _ _ is the solution of equation 2x+y = 4, and _ _ is the solution of equations. It is suggested to substitute three groups of values respectively. ( 1),(3); (1). Notes about the solutions of equations must be the same solution of each equation in the equation.

3. It is known that it is the solution of the equation x+2my+7 = 0, then m = _ _ _ _ _ It is suggested to substitute into the equation to find m, and the answer is-.

4. If the solution of the equations is 0, then A = _ _, and B = _. It is suggested that the original equations be transformed into binary linear equations about A and B, and then solved. The answer is A =-5 and B = 3.

5. The equation Y = KX+B is known. When X = 2, Y =-2; When x =- and y = 3, then k = _ _ _ _, and b = _ _ _.

It is suggested that the corresponding values of x and y be substituted to obtain the binary linear equations about k and b.

The answer is k =-2 and b = 2. It is a common method to solve undetermined coefficients by establishing equations.

6. If | 3a+4b-c |+(c-2b) 2 = 0, then a: b: c = _ _ _ _ _.

It is suggested that 3a+4b-c = 0 and c-2b = 0 from the non-negative nature. Then a and c are represented by an algebraic expression containing b, and the values of a=- b and c can be obtained. The answers are a =-b and c = 2b. A: B: C =-2: 3: 6.

It is a common and effective method to express the remaining unknowns by algebraic expressions of unknowns.

7. When m = _ _ _ _ _ _, the equation X+2y = 2, 2x+y = 7 and MX-y = 0 have a common * * * solution.

It is suggested to solve the equation first, substitute the values of x and y into the equation MX-y = 0, or solve the equation.

The answer, m =-. Comment on "common * * * solution" is the basis of establishing equation.

8. A three-digit number is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Prompt to multiply the number on each number by the corresponding number, and then sum.

The answer is 100x+ 10y+2 (x-y).

(2) Multiple choice questions (2 points for each small question, *** 16 points):

9. The following equations are known: (1), (2), (3), (4),

Among them, the number of binary linear equations is .............................................. ()

1 (B)2 (C)3 (D)4

It is suggested that equation group (2) contains three unknowns, and the degree of y in equation group (3) is not 1, so neither (2) nor (3) is a binary linear equation group.

10. Assuming that 2xB+5Y3A and -4x2AY2-4B are similar projects, the value of ba is ........................... ().

(A)2 (B)-2 (C) 1 (D)- 1

Prompt is defined by similar items, so ba = (- 1) 2 = 1. Answer C.

1 1. Suppose the solution of the equation is, then the values of m and n are ... ().

(A) (B) (C) (D)

It is suggested that the binary linear equations about m and n be substituted into the equation to solve. Answer D.

12. The solution of the ternary linear equations is .................................... ().

(A) (B) (C) (D)

It is suggested to add the two sides of the three equations separately to get x+y+z = 6 or substitute the options into the equations one by one for verification.

X+y = 1 (b) and (d) are all wrong; Then y+z = 5, which excludes (c), so (a) is correct, and the former solution is called direct method; The latter solution is called inverse verification method. Answer a.

Comments Because the multiple-choice questions in mathematics are mostly single-choice questions-there is only one correct answer, it has one more known condition than the general questions: one and only one of the multiple-choice questions is correct. Therefore, there are many special solutions to multiple-choice questions besides direct method. With the deepening of the study, we will introduce them to the students one by one.

13. If the values of the solutions x and y of the equation are equal, the value of a is .................... ().

(A)-4 (B)4 (C)2 (D) 1

It is suggested that X = Y be substituted into 4x+3Y = 14 to get X = Y = 2, and then substituted into the equation containing a. Answer C.

14. If the solution of the equation about x and y satisfies the equation 2x+3y = 6, then the value of k is ().

(A)- (B) (C)- (D)

It is suggested that k should be regarded as a known constant, and the values of x and y can be found, and then the values of x and y can be substituted into 2 x+3 y = 6 to get K. Answer B.

15. if the equation y = kx+b, when x and y are reciprocal, b is smaller than k 1, and x =, then the values of k and b are ..........................................................................................................

(a) 2, 1 (b), (c)-2, 1 (d),-the answer d can be given by the known x =, y =-.

16. Students in a class participate in activities in groups. If there are 7 students in each group, the remaining 4 students; If there are 8 people in each group, there are 3 people in each group. If there are X students in the class and they are divided into Y groups, we can get the equation ............................................................ ().

(A) (B) (C) (D)

It is suggested that the equivalence relation be drawn from the meaning of the question: (1)7 groups of people = total number-4; (2) Number of people in 8 groups = total number +3. Answer C.

(3) Solve the following equation (4 points for each small question, 20 points for * * *):

17. it is suggested to eliminate x by addition, subtraction and elimination. Answer.

18. It is suggested to sort out the equation first, turn it into an integral coefficient equation, and eliminate x by addition and subtraction.

19. It is suggested that x = y be obtained from the first equation, and the offspring should be sorted into the second equation; Or from the first equation, let x = 2 k, y = 5 k, and substitute it into another equation to find the value of k, the answer.

20.(A and B are nonzero constants)

It is suggested that the left and right sides of the two equations should be added separately to get X+Y = 2A1, and both equations should be used to solve ① at the same time.

answer

Comment on superposition elimination method is a common method to solve the rotation equation of unknown system.

2 1.

It is suggested that the first equation should be merged with the other two equations, and y should be eliminated by addition.

answer

It is the key to choose an appropriate solution to the problem by commenting and analyzing the composition characteristics of the coefficients of the unknown items in the equations that make up the equations. Therefore, it is necessary to observe carefully before solving the problem, in order to find out the shortcut to solve the problem.

(4) Problem solving (6 points for each small question, *** 18 points):

22. Given that the sum of solutions X and Y of the equation is 12, find the value of n. 。

It is suggested to solve the known equation, express x and y with algebraic expression of n, and then substitute x+y = 12.

Answer n = 14.

23. Assuming that the equation and the solution are the same, find the value of A2+2AB+B2.

It is suggested to solve the equation first to get x and y, and then substitute it into the equation to get a and b.

The answer.

Note When the solutions of n equations are the same, any two equations can be combined into a new equation.

24. It is known that when x = 1 and x =-3, the algebraic expression x2+ax+b has values of 0 and 14, respectively. Find the algebraic value when x = 3.

It is suggested that the equations about a and b can be obtained from the meaning of the question. Find a and b, write this algebraic expression, and then find its value when x = 3.

Answer 5.

Comment on this example. After calculating the values of A and B by the undetermined coefficient method, you should write this algebraic expression, because this is the key step of evaluation.

(5) Solving problems in the application of equations (every 1 item 10, 20 points * * *);

Last year, there were 80 more boys than girls in the first grade of a school. This year, the number of girls has increased by 20%, while the number of boys has decreased by 25%. As a result, there are 30 more girls than boys. How many boys and girls were there in Grade One last year?

It is suggested that there were x boys and y girls in senior one last year, and the equation can be obtained.

The answer is x = 280 and y = 200.

26. The distance between A and B is 20 kilometers. A and B go in opposite directions from A and B at the same time and meet on the road two hours later. Then A returns to A and B moves on. When A returns to A, B is 2 kilometers away from A. Find the speed of A and B. 。

According to the meaning in the question, A walked for 2 hours before they met. "When A returned to A, B was 2 kilometers away from A." We can get another equality relationship of the equations: A and B walked in the same direction for 2 hours, with a difference of 2 kilometers. Let the velocities of A and B be X km/h and Y km/h respectively, then