Urgent!! Solve problems with a system of binary linear equations

1. Set X tons of water for A and Y tons for B.

3x=5y8*

The solution yields x=15 2 and y=9 2

A should pay $4*.

B shall pay dollars. 2. Set up to buy 3 pieces of x people, 2 pieces of y people, then one piece of 33-x-y people, get.

3x+2y+(33-x-y)=76

33-x-y)+ where the original unit price is in units of 1).

Solve the system of equations.

If you have any questions, please ask; If you are satisfied, thank you!

Question 1, first of all, it is very clear that it is required to use a binary equation to solve the problem, then it is necessary to set the water consumption of A and B as x and y, then the column formula, this is a problem again, there are two forms of water bills, which column is used?

If it is assumed that both A and B are more than 4 tons of water, then according to the calculation of each ton of water, the > 4+4 is not true, so this situation is not valid.

Because A:B = 5:3 (that is, B uses less water), there are two types of columns.

First, when y<4 and x>4 are x:y=5:3, the solution must meet the assumptions.

Second, when x>4,y>4 has x:y=5:3,8*, the solution must meet the assumptions.

Question 2, first of all, it is very clear that the customers who buy 3 pieces and buy 2 pieces are x and y people respectively.

According to the title: 3x+2y+(33-x-y)*1=763x*

Use white iron sheet to make canned food boxes, each iron sheet can be made into 25 box bodies, or 40 box bottoms, a box body and two box bottoms are matched into a set of canned food boxes, the existing 36 white iron sheets, how many pieces of box body are used, how many pieces of box bottom can make the box body and the bottom of the box just match?

Analysis: Because there are now always 36 tin box bodies and bottoms. So x+y=36

Formula; The number of sheets of the body of the box + the number of sheets of the bottom of the box = the total number of sheets of white iron sheets made of canned food boxes 36Equation (1) is derivedAnd because now a box body and two box bottoms are matched to form a set of canned food boxes.

So; The number of boxes * 2 = the number of boxes at the bottom. This will make them equal. Equation (2) 2*16x=40y is obtained

x+y=36 (1)

2*25x=40y (2)

36-y=x (3) from (1).

Substitute (3) for (2);

50(36-y)=40y

y=20 and y=20 are substituted into (1) to obtain: x=16

So; x=16

y=20A: Use 16 sheets to make the body of the box, and use 20 to make the bottom of the box.

2. The road from A to B has a section of uphill and a flat road. If you keep the uphill slope at 3 km/h, the flat road at 4 km/h, and the downhill slope at 5 km/h, it will take 54 minutes to get from A to B, and 42 minutes to get from A to A. How much is the journey from A to B?

Solution: 54 minutes = hours, 42 minutes = hours.

Set up an uphill road A km and a flat road B km, according to the theme.

a/3+b/4=

a/5+b/4=

Subtract the two formulas. a(1/3-1/5)=

a=substitution for (1)b=

So the distance from A to B = km.

3. Use two antiseptic potions containing 30% and 75% to prepare 18kg of preservative solutions containing 50% medicine.

Solution: Add a kilogram of potion containing 30% of the medicine and 75% of b kilogram.

30%a+75%b=18×50%（1）

a+b=18（2）

Substitute (1) by (2) a = 18-b

b = 8 kg.

a = 18-8 = 10 kg.

Therefore, 10 kg of 30% medicine and 8 kg of 75% medicine are required.

1。Set x sheets to make the box body, Y sheets to make the bottom of the box, then x+y=36, 2*25x=40y, the solution is x=16, y=20

First, the premise of this question should be that x is equal to a positive integer.

x²-3x-2=0

Solution: x(x-3)=2 is obtained from the original formula

When x=1, x-3=2, x1=1, x2=5 (in this case, 1 or 2 is the representative of two different values of x).

Since , is the two roots of the equation, then there is: when =1, =5:

Algebraic +3 +2 =126

When =5, =1:

Algebraic +3 +2 =30

When x=2, x-3=1, x1=2, x2=4

Then there is : when =2, =4:

Algebraic +3 +2 =84

When =4, =2:

Algebraic +3 +2 =36

To sum up: When x1 = 1 and x2 = 5, there is: algebraic formula +3 +2 = 126 or algebraic formula +3 +2 =30

When x1 = 2 and x2 = 4, there is: algebraic +3 +2 =84 or algebraic algebraic +3 +2 =36

Question 2: When the apple falls to the ground, the distance from the ground is 0, then h(m)=0, and 0 is brought into the original formula h=125-5t, 125-5t=0

then, t = 5, we get t1 = 5 and t2 = -5

Since t is time, t cannot be negative, but can only be 5

So t=5 Question 3: We can set the annual interest rate of the first deposit to be x, then the annual interest rate of the second deposit is y=90 x

It can be seen from the question that if there is no interest, then Xiao Ming's money is 1000-500=500

But Xiao Ming's money has increased by 30 due to more interest, you can think of the interest of the first year + the interest of the second year = 30

You can list the equation 1000x+500 multiplied by 90%x=30

then x is approximately equal to.

Converted to a percentage, x is approximately equal to.

If , are the two roots of the equation x -3x-2 = 0, find the value of the algebraic equation +3 +2.

x²-3x-2=0

x=(3±√17)/2

Set: one-day tour x people, three-day tour y people.

Two equal relationships: the number of people and the number of money.

x + y = 1600

150x + 1200y = 1290000x = 600 people.

y = 1000 people.

Solution: If there are A people on a one-day trip, there will be 1600-A people on a three-day trip.

150a+（1600-a）*1200=1290000150a+1920000-1200a=1290000150a+1920000=1290000+1200a630000=1050a

a=6001600-600=1000 people.

Solution: Set up to receive one-day tourists x people, three-day tourists y people, then:

x+y=1600

150x+1200y=1290000

Launch x=600, y=1000

1) It costs X yuan to buy a shuttlecock.

Well, the purchase of pockets needs (x + yuan.

3*（x+7*x+

x = i.e.: a shuttlecock yuan, a pocket 3 yuan.

2) You can buy x pockets and y shuttlecocks.

And: y=<159

Then the matching schemes are:

x<=1；y=1

x<=2；y=2

x<=3；y=3

x<=4；y=4

x<=5；y=5

x<=6；y=6

x<=7；y=7

x<=8；y=8

x<=8；y=9

x<=10；y=10

x<=11；y=11

x<=12；y=12

x<=13；y=13

x<=14；y=14

x<=15；y=15

x<=16；y=16

x<=17；y=17

x<=18；y=18

x<=19；y=19

x<=20；y=20

x<=21；y=21

x<=22；y=22

x<=23；y=23

x<=24；y=24

x<=25；y=25

x<=26；y=26

x<=27；y=27

x<=28；y=28

x<=28；y=29

x<=28；y=30

x<=27；y=31

x<=26；y=32

x<=25；y=33

x<=24；y=34

x<=23；y=35

x<=23；y=36

x<=22；y=37

x<=21；y=38

x<=20；y=39

x<=19；y=40

That's all for the plan, haha, you're too powerful, landlord!

The rest will be answered another day, remember to give points!

(2) Solution: Set the original planned charter as X.

9(x-1)=6(x+1)

9x-9=6x+6

9x-6x=6+9

3x=15x=5(5-1) 9=36 (person) Answer: There are 36 students in the class.

How to solve a system of binary equations!

Wind speed: Let the wind speed be x and the speed of the aircraft be y.

x+y）×y-x）×13=9750

Let the aircraft speed v1, wind speed v2, downwind (v1+v2)*, headwind (v1-v2)*13=9750The simultaneous equation is solved v1 = 4275 v2 = 3525

(1) x+y=20 x-y=16 solution: x=18 y=2

2) Suppose: A walks x kilometers per hour, B travels y kilometers per hour 3x + 5y = 36

Solution: x=6 y=

x-y=16 （2） （1）+(2)：x=18 （1）-（2）：y=2

2.Let the speed of A be x km/h and B be ykm/h.

3x+5y=36 x=6 y=

Solution: 1: x y 20.........

x－y＝16………

Got: x 18

Got: y 2

2: Let the speed of A be x kilometers per hour and the speed of B be y kilometers per hour.

2＋3x＋（2＋3）y＝36

Solution: x=6 y=

1、x+y=20 x-y=16,x=18 y=2

2. Let the velocity of A be x and B be y, 3(x+y)+2y=36, then x=6,y=

1. v shun = v ship + v water v inverse = v ship - v water This problem v shun = 20 v inverse = 16 column equation v ship = 18 v water = 2

2. (A + B = 36.)

3v A + (2 + 3) v B = 36

1 x+y=20

x-y=16

x=18 y=2

2 Set the speed of the armor to xB's velocity is y

2x+2y+3(x+y)=36

x= y= it's the weekend again.

x+y=20

x-y=16

The hydrostatic velocity is 18 and the water velocity is 2

3x+5y=36

x=6y=

The two teams A and B originally excavated a total of 45 5 = 9 meters per day.

A turned out to be staring or digging every day (Kai Zai 9+ meters.

B used to dig rice every day.

The original time = 1755 9 = 195 days.

Now with a clump of oak = (1755-45) (days.

Fewer days = 195-180 = 15 days.