Ax+by=c (where a, b and c are known numbers, a≠0, b≠0) is called a binary linear equation.
A pair of x and y values that make the left and right sides of a binary linear equation equal is called the solution of this equation. expressed as
x=m
The form of. Generally speaking, a binary linear equation has countless solutions.
y=n
Secondly, two binary linear equations with the same unknowns are combined to form a binary linear equation group, and their common solution is called the solution of this binary linear equation group.
change
Substitution elimination method or addition and subtraction elimination method
Application of binary linear equation;
The key: find out two independent equality relations contained in the problem, and then set two unknowns and list the equations formed by the two equations to solve it.
Note: the results should be tested to see if they conform to the actual problems.
Comprehensive self-improvement 2:
Multiple choice
1. Of the following four equations, () belongs to a system of binary linear equations.
A.2x-y=5 B.2x-y=5 C.x+2=3 D 2x-y=5
y+z=8 y-x=3 xy=z
2. In x=0 x= 1 x=5 x=3, there is a solution () that is not the equation 3x-2y= 1 1.
y=- y=-4 y=2 y=
A. 1 Group B.2 Group C.3 Group D.4
3. If the solution of equation 2x+y=0 is also the solution of equation 6x+ky=4, then the value of k is ().
x-2y=5
A. 1/5
4. It is known that the equation 5x+y=3m satisfies the solution of 2x+y=3 with respect to x and y, then the value of m is ().
x-y=m
A.- 1 B. 1 C.3 D.0
5. When x = 0, 1 and-1, and the values of quadratic trinomial ax2+bx+c are 5,6 and 10, respectively, then the values of a, b and c are ().
a=3 b=-2 c=5 B
C.a=-2 b=3 c=5 D.a= b= c=5
6. Equation │x│=y-2
The solution of 3│x│=6-y is ()
A.x = 1b.x = 1 or x=-1c.x = 1 or x =- 1d.x = 1 or x =-/kloc-.
y = 3y = 3y =-3y = 3y = 3y =- 1y = 1(
7, a store into a batch of goods, the purchase price of each commodity is one yuan, if calculated at 20% of the profit, the retail price of each commodity should be set at ().
A.20% (yuan) B. (1-20%) A. (yuan) C.A./(1-20%) D.A. (yuan)
8. The perimeter of a rectangle is 10, and the length is less than twice the width times 1. If the length is x and the width is y, the appropriate equations are ().
A.x+y=5 B x+y=5 C x+y=5 D x+y=5
y = 2x+ 1x+ 1 = 2y x = 2y- 1x = 2y- 1
9, a two-digit number, the sum of its ten digits and four digits is still equal to these two digits, such a two-digit number is ().
A.4 B.3 C.2 D. 1
Second, fill in the blanks
1, the basic idea of solving multivariate linear equations is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
2. If a-b=2, then 9-3a+3b = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
3. Write any set of positive integer solutions and any set of negative integer solutions of equation 2x-y = 3 _ _ _ _ _ _ _ _.
4. If (2x-y+ 1)2 and │x+y-5/2│ are antonyms, then x = _ _ _ _ _ _ _ _ _ _.
5. Write a set of binary linear equations with x=3 as the solution
y= -2 _____________ .
6. If the sum of two numbers is 2 1 and the difference between the two numbers is 9, then the smaller number of the two numbers is _ _ _ _ _ _ _ _ _ _ _.
Third, answer questions.
1, solve the equation (x+y)/2 = 6-(x-y)/3 12, and x+y = 2 12.
4(x+y)-5(x-y)=2 ② x-y=4 ②
3. It is known that x= 1 is the solution of the system of equations 3x-4y-m=0. Find the values of m and n ..
y= -2 2x+ny- 10=0
4. Assuming that the equations 2x-y=3 and ax-by=2 have the same solution, find the value of 3a-2b.
ax+by= 1 3x+2y= 1
Fourth, practical problems:
1. A depositor deposits two kinds of interest, * * * 20000 yuan. The annual interest rate of deposit A is 3%, and that of deposit B is 1.5%. Savers earn 525 yuan a year. How much are the two kinds of deposits (excluding interest tax)?
2. The sum of the purchase prices of the two commodities, A and B, is 100 yuan, which is sold at a discount for promotion. You can still earn 50 yuan if A is 20% off and B is 60% off. You can earn 19.5 yuan if you get a 60% discount on goods A and a 20% discount on goods B. What are the original purchase prices of A and B?
A shopping mall plans to allocate 90,000 yuan to buy 50 TV sets from a manufacturer. It is known that this manufacturer produces three different models of TV sets, the ex-factory price is RMB 0.5 million per set, RMB 2 1.0 million per set, and RMB 2,500 per set.
(1) If the shopping mall buys 50 TV sets of two different models at the same time, and it costs 90,000 yuan, please study the shopping plan of the shopping mall;
2) If a shopping mall sells a first-class TV set with a profit of 150 yuan, a second-class TV set with a profit of 150 yuan and a third-class TV set with a profit of 250 yuan, which purchase scheme is the most profitable when buying two different TVs at the same time?
4. Party A and Party B practice running. If Party B runs 10 meter first, Party A will catch up with Party B in 5 seconds; If you let B run for 2 seconds first, then A will catch up with B in 4 seconds and find the running speeds of A and B. ..
5. In a math exam, * * * has 16 multiple-choice questions. The grading method is: give 6 points for answering a question correctly, deduct 2 points for answering a question incorrectly, and give no points for not answering. A student has an unanswered question, so how many questions can the student answer correctly before his score is higher than 60?
6. Yantai big cherry is famous all over the country, and it has a bumper harvest this year. A large supermarket bought a batch of big cherries from the big cherry production base, and the quality lost 5% during transportation (the supermarket is not responsible for other expenses).
(1) If the supermarket raises the price by 5% on the basis of the purchase price, will the supermarket lose money? Explain by calculation.
(2) If the supermarket wants to make a profit of at least 20%, what percentage should the minimum price of big cherry be increased?
Choose to do the problem: the equation ax-y=2x+3 is a binary linear equation about X and Y, and find the value range of A.
(Haidian District Senior High School Entrance Examination in 2004)
In April, 2004, China Railway increased its speed for the fifth time. Assume that the average speed of K 120 air-conditioned express train is 44 km/h higher than that before the speed increase, and the train running schedule before the speed increase is shown in the following table.
The start time and arrival time of the train in the exercise interval last for the whole mileage.
A-B K 120 2: 00 6: 00 4 hours 264 kilometers
Please fill in the train timetable after speeding up according to the information provided by the topic, and write out the calculation process.
The start time and arrival time of the train in the exercise interval last for the whole mileage.
A-B K 120 2: 00 264 km