Please help me solve a junior high school problem of binary equations

by 2x+3y=4

4x-3y=2

Solution: x=1

y=2 3 is substituted for ax-by=4

ax+by=4

Get: a-2 3b=4

a+2/3b=4

Solution: a=4

b=0 So if the solution of the binary system of linear equations {ax-by=4 2x+3y=4 is the same as {ax+by=4 4x-3y=2, then a=4, b=0

The solution of the system of equations {ax-by=4 2x+3y=4 is the same as {ax+by=4 4x-3y=2.

United. 2x+3y=4

4x-3y=2

Solution. x=1

y=2 3 substitutes x=1, y=2 3.

ax-by=4

ax+by=4

a-2/3b=4

a+2/3b=4

Solution. a=4b=0

Because their solutions are the same, any two of them can form a system of equations, so use 2x+3y=4,4x-3y=2 to form a system of equations, find x,y, and then substitute the values of x,y into ax-by=4, ax+by=4, to get a system of binary linear equations about a and b, and solve a,b

1)ax-by=4

2)2x+3y=4

3)ax+by=4

4)4x-3y=2

2) Formula + (4) gives the following formula: 2x+3y+4x-3y=4+2, that is, 6x=6, so x=1

Replace x=1 as in (2) or (4) to find y=2 3.

Therefore, equation (1) is: a-2b 3=4

Therefore, equation (3) is: a+2b 3=4

The two equations get 2a=8, so a=4, then b=0

Solution: 3x-3=y+5(1).

5y-5=-3x-15（2）

From (1) we get 3x=3+y+5

8+y substitution (2) to get 5y-5=-(8+y )-15 to get y=-3 substitution (1) to get x=5 3

3x-3-y=5

5y-5+3x+15==

That is, 3x-y=8 and 3x+5y=-10

Subtracting the two formulas yields -6y=-18, so y=3 is substituted to get x=11 3

1. Add all the two formulas to get 10000 (x + y) = 50000 x + y = 5

1641x+1641y=8205, subtract with the second formula, and get 6718y=13436

y=2, so x=3

8359x+1641x=10000x -8359y+1641y=10000y =28359+21641=50000

Approximate x + y = 5

Then bring xy in - or =

The result of xy is y=2x=3

Substituting (-2,-4) and (1,5) into ax+by=5 gives -2a - 4b = 5 (1).

A + 5b = 5 to get a = 5 - 5b and a = 5 - 5b to (1).

Get 10b - 10 - 4b = 5 b = so a = 5 - =

The binary linear equation is + y = 5

Yes, I'll give you an idea because of the typing problem, I won't count the math, you can do the math yourself.

First of all, we can bring (-2,-4), 1,5) into the equation based on known conditions.

2a-4b=5 and a+5b=5

Then solve this binary system of equations, and I won't solve it.

You can calculate a b.

In addition, I would like to remind you that there are two unknowns in the problem, and if there are three unknowns, you need to use three equations to solve them, and if there are three unknowns, you need to use three equations to solve them

Substitute these two coordinates into the equation.

2a-4b=5

a+5b=5

The solution is: a=-15 2;b=5/2

So the binary equation is:

15a 2+5b 2=5 i.e.

15a+5b=10

-2a-4b=5 (1)

a+5b=5 (2)

Multiply Eq. (2) by 2 to get 2a+10b=10 (3) (3) +(1) to get 6b=15 to get b=

Substituting (1) yields -2a-4*

2a=5+10 to get a=

These two points satisfy the equation, then the substitution is the same.

Substituting two points into the equation yields: -2a-4b=5

a+5b=5

To solve these two equations, the second equation *2 + the first equation gives 6b = 15, b = 5 2 substitute the value of b into the second equation, and obtains, a=-15 2

Solution: Substituting two points into the equation is obtained.

2a-4b=5 ①

a+5b=5 ②*2

Lianli.

2a-4b=5③

2a+10b=10④

The solution is a= b=

The equation is.

1.Greater than 50

2.Relieve boredom and accept Zen reputation; Set up a regiment of ants to attack x people, to group y people.

13x+11y=1392

9x+9y=1080

solution; x=36 y=84

Answer: Let the uphill distance be x km, the flat road distance be y km, and the downhill distance be z km

x+y+z=142………

x/28+y/30+z/35=

z/28+y/30+x/35=

Subtract y from - to get z=28+x

Then z=28+x can be substituted into the formula to get y=114-2x

Substituting z=28+x and y=114-2x yields: x 28+(57-x) 15+(28+x) 35=

Then go to the denominator and solve the unary equation of x, which has only one unknown, and get x=42

Then substituting x=42 into y=114-2x and z=28+x yields: y=30, z=70

So the final solution is 42 kilometers uphill, 30 kilometers on the flat road, and 70 kilometers downhill

A store gave 76 backlogs** to 33 customers, with each customer buying a minimum of 1 and a maximum of 3 items. Buy 1 piece at the original price, 2 pieces 90% discount, 3 pieces 20% discount. As a result, it is equivalent to 76 items all of which are discounted by 85%.

Ask how many customers are buying 2 pieces and 3 pieces.

If you buy two pieces have x, three pieces have y, and one piece has 33-x-y

33-x-y+。8y*3=76*

4x+7y=158

x=158/4-7y/4

Since x is an integer, 158 4 = 39... 2

Then the remainder of 7y 4 is 2

y=2, x=36, does not match the topic.

y=6, x=29, not in line with the title.

y=10, x=22, that is, there are 22 people who buy two pieces and 10 people who buy three pieces.

In addition, there are the following cases:

y=，y=18，x=8

y=22，x=1

You didn't learn the first problem upstairs, you didn't learn, and the second problem is wrong.

1) The time spent coming and going on the flat road is the same, so the difference in the time of coming and going is on the slope, the time to go is less than the time to come back, so when you go downhill than uphill, we set the downhill road when you go to x kilometers more than the uphill road, then there is.

x/28-x/35=

x=28 so we can let the uphill road have x kilometers, then the downhill road has (x+28) kilometers, and the flat road has y kilometers, then.

x+(x+28)+y=142……The total distance is 142 km) y 30 + x 28 + (x + 28) 35 = hours of time at the time of going) solves: x=42, y=30

So the flat road is 30 km, the uphill distance is 42 km, and the downhill distance is 70 km.

2) If there are x people who buy 3 pieces, and there are y people who buy 2 pieces, then there are (33-x-y) people who buy 1 piece, and the unit price of each piece is 1.

Total**)3x+2y+33-x-y=76......A total of 76 products) solves: x=14, y=15

1.Set the uphill x km and downhill y km when you go up, and (142 - x - y) km on the flat road, and reverse the uphill and downhill when you come back.

x / 28 + y / 35 + 142 - x - y ）/ 30 =

x / 35 + y / 28 + 142 - x - y ）/ 30 =

2.X people who buy 3 pieces, Y people who buy 2 pieces, then (33 - x - y) people who buy one piece, and the unit price of one product is A yuan.

3x + 2y + 33 - x - y ）= 76

3x + 2x + a×（33 - x - y）=

1) 66x+17y=3967

25x+y=1200

Answer: x=48 y=47

2) 18x+23y=2303

74x-y=1998

Answer: x=27 y=79

3) 44x+90y=7796

44x+y=3476

Answer: x=79 y=48

4) 76x-66y=4082

30x-y=2940

Answer: x=98 y=51

5) 67x+54y=8546

71x-y=5680

Answer: x=80 y=59

6) 42x-95y=-1410

21x-y=1575

Answer: x=75 y=48

7) 47x-40y=853

34x-y=2006

Answer: x=59 y=48

8) 19x-32y=-1786

75x+y=4950

Answer: x=66 y=95

9) 97x+24y=7202

58x-y=2900

Answer: x=50 y=98

10) 42x+85y=6362

63x-y=1638

Problems of binary systems of linear equations:

It is mainly a practical problem.

There are also these.

A circle is the set of all points whose distance to a fixed point is equal to a fixed length.

First of all, you have to understand that a line is made up of an infinite number of points.

The distance from any point on the circle to the center of the circle is equal to the radius.

"Fixed point" is the center of the circle, and "fixed length" is the radius.

A "set" is actually a graph made up of these points.

What is the use of the x-axis and y-axis?

Both the x-axis and y-axis are part of a planar Cartesian coordinate system.

Draw two number axes that are perpendicular to each other and have a common origin in a flat "2D". Abbreviated as Cartesian coordinate system. The planar Cartesian coordinate system has two coordinate axes, of which the horizontal axis is the x-axis (X-axis), and the orientation to the right is the positive direction; The vertical axis is the y-axis, which you should look at here.

1) 150m, set fast speed x, slow speed y, 20x-20y = 70 + 80

2) 150m, set fast speed x, slow speed y, 4x+4y=70+80

3) The combination of two equations 20(x-y) = 4(x+y), so 2x=3y, so x=3y 2, bring x=3y2 into the above equation, so 10y=150So y=15, x=, done.

Just did this question, help you o( o

1）150 20x-20y=150

2）150 4x+4y=150

3) Solution: Let the fast train be x meters per second, and the slow train be y meters per second.

4x+4y=70+80

20x-20y=70+80 solution: x=

y=15