Binary Linear Equations Solved! Just a system of equations!

4.Let the velocity of A be x meters and the speed of B be y meters.

30x-30y=300 x-y=10①

2x+2y=300 x+y=150②

Get 2x=160

x=80 - 2y=140

y=70A: A's speed is 80 meters, and B's speed is 70 meters.

5.The distance at the time of departure is xkm, minutes = hours.

x+3)/(15+1)-x/15=

x+3)/16-x/15=

15(x+3)-16x=30

15x+45-16x=30

16x-15x=45-30

x=15A: The distance at the time of departure is 15km.

6.Let the train be x meters long and y meters per second.

1000+x=60y 60y-x=1000 1000-x=40y 40y+x=1000 + get 100y=2000

y=20 substituting 60 20-x=10001200-x=1000

x=1200-1000

x=200A: This train is 200 meters long and has a speed of 20 meters per second.

Intelligence boost. Let the distance between AB and B be x meters, C and B will meet in y minutes, and C and A will meet in Y+10 minutes.

x=(110+125)y x=235y①

x=(100+125)(y+10) x=225y+2250 Substituting yields 235y=225y+2250

235y-225y=2250

10y=2250

y=225③

substitution x=235 225

x=52875

A: The distance between the two places is 52,875 meters.

5. Set the distance to be x and the time to go is y

Then: (x+3) 16-3 28=y

x/15=y

Solution: x=255 7 y=17 7

6. Set the length of the car to be x meters, and the speed is y meters and seconds.

Then: 2x+1000=60y

40y=1000-x

Solution: x=1000 7 y=150 7

1. Let it take y minutes to meet B, and the distance between AB and B is X meters.

Then: 125y+110y=x

125 (y+10)+100(y+10)=x, x=52875 y=225

Multiplying an equation by a number at the same time or dividing it by a number will not change, sometimes the equation is multiplied by a number at the same time to make it easier to calculate, or the teacher will make it easier for you to understand.

The system of binary equations is mainly eliminated (that is, two unknowns become one unknown), and there are two main elimination methods, 1 is substituted for the elimination method, and 2 is the addition and subtraction elimination method. Take the example you gave: if you use the substitution elimination method, the calculation will become more complicated, and the steps are as follows:

2x+3y=16 can become 2x=16-3y and then x=(16-3y) 2, and then substituting this into 3x-2y=11 will give 3*(16-3y) 2-2y=11, so that a binary equation will become a univariate equation.

Take a look at addition, subtraction, and elimination:

Let 3x-2y=11 be Equation 1 and 2x+3y=16 be Equation 2

Equation 1*3 is equal to 9x-6y=33, and equation 2*2 is equal to 4x+6y=32. (Why is Equation 1 multiplied by 3 and Equation 2 multiplied by 2?) Because the coefficient of y is the same, the unknown number y is eliminated).

Add Equation 1 to Equation 2 9x-6y+4x+6y=33+32

You can do the rest yourself.

Multiply the equation 3x-2y=11 to obtain, (reason: multiply the same number on both sides, the value does not change, and the addition and subtraction should be used, so it paves the way for the following).

Add the equation to 2x+3y=16 to get it.

x = 5 and substituting x = 5 into the original equation 2x + 3y = 16 (or 3x-2y = 11) to get y = 2

So the system of equations x=5, y=2 is the solution of the equation.

The answer to the question is explained during the solution process).

How to solve a system of binary equations!

Add and subtract the same coefficient and multiplier for ease of calculation.

It's almost forgotten.,Seek Y first and that's probably it:

x=(11+2y)/3

x=(16-3y)/2

3(16-3y)=2(11+2y)

48-9y=22+4y

48-22=4y+9y

y=2x=5

x=5 y=2

Equation 1: 3x-2y=11 times 3

Eq. 2 2x+3y=16 multiplied by 2

So that both formulas have 6 y, and then the two formulas are added to cancel the y, so that there is only one unknown number left in the formula, x, and the answer can be found by solving the unary method.

3x-2y=11 multiplication of each item by 2 is 1: 6x-4y=22 2x+3y=16 multiplication by 3 is 2: 6x+9y=48 then 1-2 gives -13y=-26 finds y=2 and then takes the calculated y into any of the original equations to get x=5 while multiplying a number to determine that one of the two variables has the same pending coefficient, then one variable can be removed and the remaining way about one independent variable is solved, and the solution of the other variable is obtained.

1、(x+y)/2+(x-y)/3=1，3x+3y+2x-2y=6,5x+y=6

4(x+y)-5(x-y)=2,5y-x=2y=8/13,x=14/13

2. When solving the system of equations ax+5y=15 4x-by=-2, due to carelessness, A Lancao took a in the system of equations, and obtained the solution x=-3, y=-1, and B misread the b in the system of equations, and obtained the solution as x=5, y=4.

1) A sees a as -20 3What does B think of 11 2-3a-5=, -12+b=-2,b=105a+20=15 ,a=-1,20-4b=-2,b=11 2(2) to find the correct solution to the original system of equations.

ax+5y=15 4x-by=-2,a=-1,b=10-x+5y=15,4x-10y=-2

x=14,y=

1) Solution: Let the worker who produces screws every day be x, then the worker who produces nuts every day is y.

According to the title: 2*100x=150y x+y=42 solution: x=18 y=24 that is, 18 workers produce screws per day, and 24 workers produce nuts per day.

The second question is beam collision: two objects moving on a circle with a circumference equal to 400cm, so they meet every 20s, is it the same direction? If it is a square oak volt group, the group is as follows: 20x-20y=400 10x+10y=400

1) When y = 3, the binary linear equation 3x+5y= 3 and 3y 2ax=a+2 (the equation about x, y) have the same solution, find the value of a

2) If (a 2) x + (b + 1) y = 13 is a binary linear equation with respect to x,y, then what conditions does a,b satisfy?

3) Knowing that x,y are rational numbers, and ( x 1)2+(2y+1)2=0, what is the value of x y?

1.Let A and B each x, y

8（x+y）=3520

6x+12y=3480

Solution: x=300, y=140, 300 yuan for team A, 140 yuan for team B.

2.Set A and B separately x,y days.

8/x+8/y=1

6/x+12/y=1

Solution: x=12, y=24, 12 days for team A, 24 days for team BPlan 1 costs 3,520 yuan and is completed in 8 days.

Option 2 costs 3,480 yuan and is completed in 18 days.

However, if the shopping mall of plan 1 opens 10 days earlier, it can also make a profit of 2,000 yuan, which is 1,960 yuan less than that of plan 2.

So option 1 is more conducive to shopping malls.

If team A is payable for $ x every day, and team B is payable for $ y, then according to the title:

8（x+y）=3520 ①

6x+12y=3480 ②

It's easy to figure out what follows x and y.

It's pretty simple.

1。Let one revolution be s, the speed of A is v1, and the speed of B is v2.

The following equations can be used:

s=2（v1+v2）

s=6（v1-v2）

The answer is calculated, A ran 1 3 laps, B ran 1 6 laps so you can figure out how many laps you have run.

2。Set the downhill slope to S1 and the flat to S2.

Then s1 3 + s2 4 = 54 60

s1/5+s2/4=42/60

Answer: s1 = s2 =

Hopefully, you understand how.

At the beginning, the master overhauled x units per hour. The apprentice is Y Taiwan, 6x+6y=210

2*2x=6y

solution, x=21, y=14

Set the speed of the master to be a, and the speed of the apprentice to be b

6×(a+b)＝210

2×2a＝6b

1. All 1, solution: The average speed of A and B is x, y kilometers respectively.

x+y）*1=6

x-y）*3=6

The solution yields x=4 and y=2

Answer... 2. Solution: The speed of A is a meter minute, the speed of B is B meter minutes, and the runway length is m meters at the same time and starts in the same place, going in the opposite direction, and meets every 2 minutes. In other words, the road walked by two people in two minutes adds up to a circle. then one circle is 2a+2b=m(1).

Walk in the same direction, meet every 6 minutes, and A runs faster than B. In 6 minutes, A walked one more lap than B. then one circle is 6a-6b=m(2).

1) x3 + (2) to get 12a = 4m, a = 1 3m is a run of 1 3 laps per minute, and bringing in (1) to get b = 1 6m is a run of b 1 6 laps per minute.

Let the velocity of A be x and the velocity of B be y

1 6 (x+y)= 1 3y+6= 3x, which gives x=4 y=2

2 Let the distance of a circle be s (s can be thought of as known).

2x+2y=s 6x-6y=s

The solution is x= 1 3 s y = 1 6 s, i.e., A runs 1 3 revolutions per minute and B runs 1 6 revolutions per minute.

Let the average velocity of A be x and the average velocity of B y

Then there is (x+y)*1=6

x-y)*3=6

The solution is x=4km h, y=2km h

2) Let A run x laps per minute and B run y laps per minute.

x+y)*2=1 (1 means 1 turn).

x-y)*6=1

The solution yields x=1 3 turns, y=1 6 turns.