1. When 3x+4y=9, if 2y=6, then x = _ _ _ _ _ _ _
Analysis: y=3 is obtained from 2y=6. If y=3 is substituted into 3x+4y=9, there is 3x+ 12=9, and x=- 1 is obtained.
Answer:-1
2. It is known that x=2, y= 1 is the solution of equation 2x+ay=5, then A = _ _ _ _ _ _ _ _-.
Analysis: According to the concept of solution of equations: 2×2+a 1=5, a= 1 is obtained.
Answer: 1 [Source: Xue. Part. Net]
3. The solution of the equation is ()
A.B
CD。
Analysis: Substitute four groups of values of X and Y, A, B, C and D respectively to make the left and right sides of the two equations of the equations equal, which is the solution of the equations.
Answer: c
4. Given △ABC, ∠A=x, ∠B=2x, ∠C=y, try to write the relationship between X and Y. If x=y, try to find the size of each angle.
Analysis: The equation is established according to the fact that the sum of the internal angles of the triangle is equal to 180. When x=y, it can be replaced. Find the size of each angle in the equation of y and x.
Answer: The question is: x+2x+y = 180, which means 3x+y = 180.
When x=y, there are 3x+y = 180, 4x = 180,
So x = 45, then y = 45,
So ∠ A = 45, ∠ B = 90, ∠ C = 45.
Comprehensive application
5. Because A misreads A in Equation ①, the known equation leads to the solution of the equation as x=-3, y=- 1, and B misreads B in Equation ②, leading to the solution of the equation as x=5, y=2. Try to find the values of A and B [Source: Z, xx, k.Com].
Analysis: According to the concept of the solution of the equation, we can know that x=-3, y=- 1 are the solutions of equation ②, and x = 5 and y = 4 are the solutions of equation ①, so we can get A and B by substituting them into equation ② respectively.
Answer: according to the meaning of the question, substitute X =-3 and Y =- 1 into equation ② to get:-12+b=-2.
Solution: b= 10,
Substitute x = 5 and y = 2 into equation ① to get 5a+20= 15.
The solution is a=- 1.
6. Scoring rules of football league: a game wins 3 points, 1 point, and a game loses 0 points. A team in the football league scored 6 points in four games. How many games did the team win, draw and lose?
Analysis: If the X field wins and the Y field is flat, then the negative [4-(x+y)] field, plus the * * * score (3x+y), can get the equation.
Answer: Let this team win X games and draw Y games. According to the meaning of the question, 3x+y=6.
From 0 ≤ x ≤ 4 and 0 ≤ y ≤ 4, there are: x=0, y = 6>4, impossible;
x= 1，y=3，4-(x+y)= 0； x=2，y=0，4-(x+y)= 2；
X = 3,3x = 9>6, so it is impossible;
So win 1 game, draw 3 games or win 2 games and lose 2 games.
7.(20 10 Fujian Fuzhou simulation) The solution of the equations is ().
A.B
CD。
Analysis: Substitute four groups of values of X and Y, A, B, C and D respectively to make the left and right sides of the two equations of the equations equal, which is the solution of the equations.
Answer: c
8.(20 10 simulation of Ordos, Inner Mongolia) The state implements the policy of "two exemptions and one subsidy" for students in the nine-year compulsory education stage. The following table is part of the free textbook subsidy provided by a middle school in our city.
grade
Item 789[ Total]
Free subsidy amount per person (RMB) 1 109050-
Number of people (person) 80300
Total free subsidy (RMB) 400,026,200 yuan.
If you want to know the data in the blank, you can set the number of seventh-grade students as X, the number of eighth-grade students as Y, and list the equation as () according to the meaning of the question.
A.B
CD。
Analysis: According to the data in the table, the total number of students in grades 7, 8 and 93 is 300, while the number of students in grade 9 is 80. If the number of students in grade 7 is X and the number of students in grade 8 is Y, we can easily get the equation: X+Y+80 = 300; Similarly, according to the total amount of free subsidies, we can get the equation:110x+90y+4000 = 26200, so we can get the equations: