2. In x+3y=3, if X represents Y, then Y = _ _ _ _ _ and Y represents X, then X = _ _ _ _ _

4. The general form of transforming Equation 3(x+5)=5(y- 1)+3 into a binary linear equation is _ _ _ _.

(1) equation y=2x-3 has _ _ _ _ _ _;

(2) The solution of equation 3x+2y= 1 has _ _ _ _ _ _;

(3) The common * * solution of equations y=2x-3 and 3x+2y= 1 is _ _ _ _ _.

9. Equation x+y=3 has _ _ _ group solutions and _ _ _ group positive integer solutions, which are _ _ _ _ _ respectively.

1 1. Equation (k2-1) x2+(k+1) x+(k-7) y = k+2. When k = _ _ _ _ _ _, the equation is linear; When k = _ _ _ _ _, the equation is a binary linear equation.

12. For the binary linear equation 2(5-x)-3(y-2)= 10, when x=0, then y = _ _ _ _ _ _ When y=0, then x = _ _ _ _.

13. The positive integer solution of equation 2x+y=5 is _ _ _ _ _.

14. If (4x-3)2+|2y+ 1|=0, then x+2 = _ _ _ _.

Solution.

When k is _ _ _ _ _, the equations have no solution.

____.

(2) Choose

24. in equation 2(x+y)-3(y-x)=3, if y is expressed by an algebraic expression containing x, then []

a . y = 5x-3；

b . y =-x-3；

D.y=-5x-3。

[ ]

26. The system of equations consisting of the known binary linear equation 5x-y=2 has many solutions [].

a . 10x+2y = 4；

b . 4x-y = 7；

c . 20x-4y = 3；

D. 15x-3y=6。

[ ]

Morning = 9;

b . m = 6；

c . m =-6；

D.m=-9。

28. If 5x2ym and 4xn+m- 1y are similar terms, the value of m2-n is [].

a . 1；

B.- 1;

C.-3;

D. None of the above answers are correct.

29. The solution of equation 2x+y=9 in the positive integer range is [].

a . 1；

B.2;

C.3;

D. iv

[ ]

A.4

B.2

C.-4;

D. None of the above answers are correct.

Binary linear equations? Comprehensive innovation exercise

First, comprehensive questions

z，3，2

z，3，2

3. It is known that 4ax+yb2 and-a3by are 2x-y values of similar terms.

z，3，2

4. If | x-2 |+(2x-3y+5) 2 = 0, find the values of x and y. 。

Three, three

5. If the equation 2x2m+3+3Y5n-4 = 7 is a binary linear system of x and y, find the value of m2+n. 。

z，3，2

Second, the topic of innovation

1. It is known that x and y are reciprocal, and (X+Y+4) (X-Y) = 4. Find the values of x and y.

n，4，3

2. Find the solution of equation X+2Y = 7 in the range of natural numbers.

n，4，3

Third, the mid-term exam questions

(Shandong, 95, 3 points) The following conclusion is correct.

[ ]

Reference answers and instructions

Knowledge points of 1. 1. test: the solution of equation and the value of algebraic expression.

∴ 2m+3n=2×2+3(-3)=4-9=-5。

2. Knowledge points of the test: the solution of the equation and the solution of the linear equation of one variable.

Solution: Substitute X =-3 and Y =-2 into the equation and get 2 (-3)-4 (-2)+2A x=-3.

Hugging: The knowledge points of the above two questions are similar. When the solution of the equation is known, the values of other letters in the equation can be obtained by substituting this group of numbers into the equation or equation group.

3. Knowledge points of the test: similarity terms and solution equations

Cuddle: According to the definition of similar terms, the same letters have the same index, so the equation can be listed and solved.

4. Knowledge points of the test: the nature of non-negative numbers and the simple solution of binary linear equations.

Cuddling: Because | x-2 | ≥ 0 and (2x-3y+5) 2 ≥ 0, when their sum is zero, the two numbers must be zero, that is, x-2 = 0 and 2x-3y+5 = 0.

5. Knowledge point: the definition of binary linear equation.

Solution: from the meaning of the question.

Hugging: According to the definition of binary linear equation, the exponent of unknown term is 1, from which it is concluded that 2m+3 = 1, 5n-4 = 1.

2. 1. Knowledge points of the exam: the meaning of reciprocal and the solution of simple binary linear equations.

Solution: from the meaning of the question, x+y = 0,

∫(x+y+4)(x-y)= 4。

∴ 4(x-y)=4

X-y = 1。

2. Knowledge points of the test: natural number solution of binary linear equation.

Solution: Transform the equation X+2Y = 7 to get X = 7-2Y.

Let y= 1, 2,3,4 ..., then x = 5,3, 1,-1 ...

Cuddle: Natural number solutions of binary linear equations, that is, unknowns, are all natural numbers. Firstly, the equation is deformed, and another letter is represented by an algebraic expression containing one letter, and then it is solved according to the characteristics of the topic.

Third, knowledge points: the definition of the solution of binary linear equations.

Solution: d

Hugging: according to the definition of binary linear equations, the solution of binary linear equations is the solution of every binary linear equation in the equations, so choose D.

Respondent: dingding 888888- magic apprentice level 1 5-3 1 2 1: 10.

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More questions about the exercises of binary linear equation >>

Look at the same problem: the calculation problem has an answer.

Best answer comment *** 19

okay

Commentator: Candy God of War-Probation Level 1

Is there a problem with binary linear equations?

Commentary: Spider-Man, a thunderbolt-new to Jianghu level 3.

There is no calculation problem.

Narrator: Luo Bing —— Trainee Magician Level 3

Let me comment on all the comments >> Other answers *** 1

Each equation contains two unknowns whose exponents are 1. Equations like this are called binary linear equations.

Two binary linear equations with the same unknowns are combined into binary linear equations.

The value of two unknowns that make the values on both sides of a binary linear equation equal is called the solution of a binary linear equation, which has countless solutions (except for a binary linear equation).

The common solution of two equations of binary linear equations is called the solution of binary linear equations.

How to Solve Binary Linear Equation: method of substitution and Addition and Subtraction

substitution method

An unknown number is represented by a formula containing another unknown number, and then it is substituted into another equation to get the solution of this binary linear equation group.

Addition and subtraction

When the coefficients of the same unknown in two binary linear equations are opposite or equal, the unknown can be eliminated by adding or subtracting the two sides of the two equations respectively, thus a univariate linear equation system can be obtained.

References:

The seventh grade math book book 2

(1) Fill in the blanks

1. Binary linear equation 4x-3y= 12. When x = 0, 1, 2, 3, y = _ _ _ _ _

2. In x+3y=3, if X represents Y, then Y = _ _ _ _ _ and Y represents X, then X = _ _ _ _ _

4. The general form of transforming Equation 3(x+5)=5(y- 1)+3 into a binary linear equation is _ _ _ _.

(1) equation y=2x-3 has _ _ _ _ _ _;

(2) The solution of equation 3x+2y= 1 has _ _ _ _ _ _;

(3) The common * * solution of equations y=2x-3 and 3x+2y= 1 is _ _ _ _ _.

9. Equation x+y=3 has _ _ _ group solutions and _ _ _ group positive integer solutions, which are _ _ _ _ _ respectively.

1 1. Equation (k2-1) x2+(k+1) x+(k-7) y = k+2. When k = _ _ _ _ _ _, the equation is linear; When k = _ _ _ _ _, the equation is a binary linear equation.

12. For the binary linear equation 2(5-x)-3(y-2)= 10, when x=0, then y = _ _ _ _ _ _ When y=0, then x = _ _ _ _.

13. The positive integer solution of equation 2x+y=5 is _ _ _ _ _.

14. If (4x-3)2+|2y+ 1|=0, then x+2 = _ _ _ _.

Solution.

When k is _ _ _ _ _, the equations have no solution.

______.

(2) Choose

24. in equation 2(x+y)-3(y-x)=3, if y is expressed by an algebraic expression containing x, then []

a . y = 5x-3；

b . y =-x-3；

D.y=-5x-3。

[ ]

26. The system of equations consisting of the known binary linear equation 5x-y=2 has many solutions [].

a . 10x+2y = 4；

b . 4x-y = 7；

c . 20x-4y = 3；

D. 15x-3y=6。

[ ]

Morning = 9;

b . m = 6；

c . m =-6；

D.m=-9。

28. If 5x2ym and 4xn+m- 1y are similar terms, the value of m2-n is [].

a . 1；

B.- 1;

C.-3;

D. None of the above answers are correct.

29. The solution of equation 2x+y=9 in the positive integer range is [].

a . 1；

B.2;

C.3;

D. iv

[ ]

A.4

B.2

C.-4;

D. None of the above answers are correct.

Binary linear equations? Comprehensive innovation exercise

First, comprehensive questions

z，3，2

z，3，2

3. It is known that 4ax+yb2 and-a3by are 2x-y values of similar terms.

z，3，2

4. If | x-2 |+(2x-3y+5) 2 = 0, find the values of x and y. 。

Three, three

5. If the equation 2x2m+3+3Y5n-4 = 7 is a binary linear system of x and y, find the value of m2+n. 。

z，3，2

Second, the topic of innovation

1. It is known that x and y are reciprocal, and (X+Y+4) (X-Y) = 4. Find the values of x and y.

n，4，3

2. Find the solution of equation X+2Y = 7 in the range of natural numbers.

n，4，3

Third, the mid-term exam questions

(Shandong, 95, 3 points) The following conclusion is correct.

[ ]

Reference answers and instructions

Knowledge points of 1. 1. test: the solution of equation and the value of algebraic expression.

∴ 2m+3n=2×2+3(-3)=4-9=-5。

2. Knowledge points of the test: the solution of the equation and the solution of the linear equation of one variable.

Solution: Substitute X =-3 and Y =-2 into the equation and get 2 (-3)-4 (-2)+2A x=-3.

Hugging: The knowledge points of the above two questions are similar. When the solution of the equation is known, the values of other letters in the equation can be obtained by substituting this group of numbers into the equation or equation group.

3. Knowledge points of the test: similarity terms and solution equations

Cuddle: According to the definition of similar terms, the same letters have the same index, so the equation can be listed and solved.

4. Knowledge points of the test: the nature of non-negative numbers and the simple solution of binary linear equations.

Cuddling: Because | x-2 | ≥ 0 and (2x-3y+5) 2 ≥ 0, when their sum is zero, the two numbers must be zero, that is, x-2 = 0 and 2x-3y+5 = 0.

5. Knowledge point: the definition of binary linear equation.

Solution: from the meaning of the question.

Hugging: According to the definition of binary linear equation, the exponent of unknown term is 1, from which it is concluded that 2m+3 = 1, 5n-4 = 1.

2. 1. Knowledge points of the exam: the meaning of reciprocal and the solution of simple binary linear equations.

Solution: from the meaning of the question, x+y = 0,

∫(x+y+4)(x-y)= 4。

∴ 4(x-y)=4

X-y = 1。

2. Knowledge points of the test: natural number solution of binary linear equation.

Solution: Transform the equation X+2Y = 7 to get X = 7-2Y.

Let y= 1, 2,3,4 ..., then x = 5,3, 1,-1 ...

Cuddle: Natural number solutions of binary linear equations, that is, unknowns, are all natural numbers. Firstly, the equation is deformed, and another letter is represented by an algebraic expression containing one letter, and then it is solved according to the characteristics of the topic.

Third, knowledge points: the definition of the solution of binary linear equations.

Solution: d

Hugging: according to the definition of binary linear equations, the solution of binary linear equations is the solution of every binary linear equation in the equations, so choose D.