Fill in the blanks of the ninth grade mathematics binary linear equation test questions (with answers) (1) (2 points for each blank, * * 28 points): 1. Given that (a-2) X-by | A |- 1 = 5 is a binary linear equation about x and y, then A = _ _ _ and | a |-1=. Answer A =-2, B ≠ 0.2. If | 2A+3B-7 | and (2A+5B- 1) 2 are antonyms, then A = _ _ _ _ B =-3.3. The positive integer solution of the binary linear equation 3x+2y = 15 is _ _ _ _ _ _ _ _. It is suggested to change the equation to y =. From y > 0 and x > 0, it is easy to know that x is greater than 0 and less than 5, and both x and y are integers. Answer. 4.2x-3y = 4x-y = 5, and the solution is _ _ _ _ _ _ _. Prompt to solve equations. Answer 5. Known as the solution of the system of equations, the value of m2-N2 is _ _ _ _ _ _. It is suggested to substitute into the equations to find the values of m and n. The answer is to find the values of x and y first. The answer is k = .7. If = = and a+b-c = are known, then a = _ _ _ _ _ _ _ b = _ _ _ _ _ _ _ and c = _ _ _ _ _ _. Hint is a set of equations, so you can set a = 2 k, b. C =。 Comment on setting "proportional coefficient" is a common method to solve the problem of quantity ratio 8. Solve the equations to get X = _ _ _ _ _ _, y = _ _ _ _ _, and z = _ _ _ _ _. It is suggested that according to the characteristics of the equation, the left and right sides of the three equations can be added separately to get 2 x+3 y+z=4 Z = 3. (2) Multiple choice questions (2 points for each small question, *** 16 points): 9. If the solution of the equation is reciprocal, the value of k is ... y =-1,and then it is substituted into the equation with the letter k, and the answer is D. 10/0. If all the equations about x and y are solutions of | a | x+by = 6, then the value of A+B is () (a) 4 (b)- 10 (c) Get the answer to the equations about | a |, b C. Comment on the solution of the equations about absolute value, and discuss them in different categories. 1 1. The two solutions of the binary linear equation AX+B = Y about X and Y are, then this binary linear equation is ................. () (a) Y = 2x+3 (b) Y = 2x-3 (c) Y = 2x+1(d) Y. Answer B. Comments It is a common method to find the undetermined letter coefficient by column equation. 12. according to the equation, X: y: z is ..................... () (a)1:2:1(b)1:(-2): (-1) 65433. -1) It is suggested that when solving equations, one unknown can be expressed by algebraic expressions of the other two unknowns, and then it can be solved according to the nature of proportion. Answer A. Note When the number of unknowns in the equations is more than the number of equations, it is feasible to treat one of them as a known constant to solve the equations. 13. If it is the solution of the equation, then the following equation holds ... () (a) a+4c = 2 (b) 4a+c = 2 (c) a+4c+2 = 0 (d) 4a+c+2 = 0. It is suggested that b be substituted into the equations to get the equations about a and c. The value of m is () (a)-6 (b)-6 (c) 1 (d) 0. It is suggested that as long as the condition of m: 2 = 3 is satisfied: (-1), the value of m can be obtained. Answer B. Comment on the equation, only if = ≦. Then the values of a and b are () (A)2, 3 (B)3, 2 (C)2,-1 (d)- 1, 2 respectively, which implies that there is a "same solution" from the meaning of the question, and the equation can be solved, solved and substituted into the equation. Find a, B. Answer B. Comments A correct understanding of the meaning of the equation "solution" is the key to establishing a solvable equation. 16. If 2a+5b+4z = 0 and 3a+b-7z = 0, the value of a+b-c is ............................... (1) 0. Solve the equations, express A and B with the algebraic expression about C, and then substitute A+B-C. Answer A. Comment on this question, or you can use the solution of whole substitution (that is, take A+B-C as a whole). (3) Solving equations (4 points for each small question, *** 16 points): 17. Solve again. Answer 18. It is suggested that the equation should be changed into the general form of the equation with integral coefficients, and then eliminated by addition and subtraction. Answer 19. It is suggested to use method of substitution, let X-Y = A, X+Y = B, then solve the equations about A and B, and then get X, Y. Answer 20. It is suggested to put the three equations on the left and right. So x-y+z = 2④. Combine ④ with the first and second equations respectively, and then calculate the values of x and z by adding, subtracting and eliminating. Answer (4) Solution (5 points for each small question, ***20 points): 2 1. Given xyz ≠0, the values to be obtained .. Y = 2 k and z = 3 k are substituted into the algebraic formula. Answer. Comments on this topic examines the flexible use of the solution of the equation and the nature of proportion. If the three elements are eliminated respectively, the equations 21y-14 z = 0,21x-7 z = 0, 14 x-7 can be obtained. Because these three equations are not independent of each other. 22. When A and B solved the equations, A misread A and got it. B wrote B of one of the equations as its reciprocal, and got the values of A and B. It is suggested that we can start from the opposite side of the question, that is, we didn't misread anything. If Party A misreads A, that is, we don't misread B, then the obtained solution should satisfy 4 x-by =-66. However, if B misspells B in an equation, it can only be determined by analysis. After judgment, B in the second equation is misspelled. The answer is A = 1 and B = 3. 23. It is known that X and Y satisfying the equations 2x-3y = m-4 and 3x+4y = m+5 also satisfy the equation 2x+3y = 3m-8. Y into 3x+4y = m+5. The answer is m = 5.24. When x = 1, 3, -2, the values of algebraic formula AX2+BX+C are 2, 0, 20 respectively. Find the values of (1)a, b and c; (2) When x =-2, the value of AX2+BX+C. It is suggested that A, B, C can be obtained from the ternary linear equations of A, B and C, and then substituted into this algebraic expression. The answer is A = 1, B =-5, C = 6；; 20. Comment on this example. If there is no first question, in principle, write this algebraic expression after finding A, B and C, and then use it to evaluate it. Finding a, b and c by using the method of undetermined coefficient is a common method to solve this kind of problem. (5) Use the column equation to solve the application problem (1 problem 6 points, the remaining 7 points, * * 20 points). It is also known that 9 times the number in percentile is less than the number in decile and the number in unit. 3. Find the original number. It is suggested that the number in the hundredth place is X, the number in the tenth place and the number in the unit are Y. According to the meaning of the question, the answer is X = 4, Y = 39, and the number in the third place is 439. Comment on this example, suppose that the number in decimal and the number in unit are different unknowns. It is easier to determine equations or solve equations. 26. Someone bought financing bonds of 4,000 yuan, one for 1 year, with an annual interest rate of 9%, and the other for 2 years, with an annual interest rate of 12%, which were withdrawn at the expiration of 1 year and 2 years, respectively, to benefit 780 yuan. How much did you buy for each of the two financing bonds? It is suggested that if one-year and two-year financing bonds are set to buy X yuan and Y yuan respectively, the answers are X = 1 200 and Y = 2 800 respectively. When commenting on this equation, it is easy to mistake the interest of two-year financing bonds for Y yuan, so it is necessary to make it clear that the question gives the annual interest rate, so the interest due in several years should be multiplied by several. If we drive 40 kilometers in the first half and 50 kilometers in the second half as planned, we can arrive on time. However, the car broke down at a speed of 40 kilometers per hour when it was 40 kilometers away from the midpoint of AB. After stopping for half an hour, I moved at a speed of 55 kilometers per hour, and finally arrived at point B on time. Find the distance between AB and the original planned driving time. It is suggested that the original plan should take x hours. Half of the distance between AB and Beijing is Y kilometers. According to the meaning of the question, the answers are x = 8 and 2y = 360. For example, half the distance from AB to Beijing is Y kilometers, and half the planned time can be X hours. Proper setting of unknowns can make it easier to establish and solve equations.