Elementary 1 math problem solving binary equations, using addition, subtraction, and elimination .

3x+y=7 ①

5x-2y=8 ②

1) 2+(2) gets:

11x=22

x=2 is substituted into (1) to obtain:

y=7-6=1

So, the solution of the system of equations is: x=2;y=1

2x-5y=-3 ①

4x+y=-3 ②

1) +(2) 5 get:

22x=-18

x=-9/11

Substituting (2) gets:

y=-3+36/11=3/11

So, the solution of the system of equations is: x=-9 11;y=3/11

6x+2y+5x-2y=14 +8

11x=22

x=2 substitution

3*2+y＝7y＝1

1) +(2) 5 get:

22x=-18

x=-9/11

Substituting (2) gets:

y=-3+36/11=3/11

So, the solution of the system of equations is: x=-9 11;y=3/11

1) x2 gets: 6x+2y=14

：11x=22 x=2

Substituting x=2 yields: y=1

The second problem is also the same thing: subtract x2 from .

1.Solution: 2, yes.

6x+2y=14

and add-on.

11x=22

x=2y=1

2.Solution: 5, yes.

20x+5y=-15

and add-on.

22x=-18

x=-9/11

y=3/11

Multiply by 2 to get 2x-2y=6

x=-10 brings the value of x into , gets.

10-y=3

y=7so.

x=-10，y=7

Add 1 to 2 to get y=7 and bring y=7 into (1) to get -x-7=3

Get x=-10

The formula is correct, and the solution is wrong.

Use (2)-(1) to get 5x=640, that is, x=128 to substitute x into (1), and solve y=3240

You see the result, right?

4x+2y=-5 （1）

3x-3y=3 （2）

1) Multiply by 3 to get: 12x+6y=-15

2) Multiply by 2 to get: 6x-6y=6

Add these two equations to give 18x=-9, so x=-1 2 (3) substituting (3) into (1) gives y=-3 2

To sum up, the solution of this equation is {x=-1 2 y=-3 2, I hope it will help you

Multiplying by 3 equals 12x+6y=-15

Multiplying by 2 equals 6x-6y=6

The sum of the two formulas gives 18x=-9 and the solution gives x=, and bringing in the original formula gives 4* the solution gives y=

4x+2y=-5 --1 3x-3y=3---2 gives 1*3 12x+6y=-15---3

6x-6y = 6---4 of 2*2

Step 3 + step 4 yields 18x=-9 x=-1 2 and substitutes -1 2 into step 1 to obtain -2 3

It's so simple to ask ......It's time for you to study.

Addition, subtraction, and subtraction.

1) Concept: When the coefficients of an unknown number of two equations in the equation are equal or opposite to each other, the two sides of the two equations are added or subtracted to eliminate the unknown, so as to turn the binary equation into a one-dimensional equation, and finally obtain the solution of the system of equations, the method of solving the system of equations is called addition, subtraction and subtraction, referred to as addition and subtraction.

2) Steps to solve a system of binary equations by addition and subtraction.

Using the basic properties of the equation, the coefficient of an unknown number in the original equation system is reduced to the form of equal or opposite numbers;

Then use the basic properties of the equation to add or subtract the two deformed equations, eliminate an unknown number, and obtain a unary equation (be sure to multiply both sides of the equation by the same number, do not multiply only one side, and then use subtraction if the unknown coefficients are equal, and add if the unknown coefficients are opposite to each other);

Solve this unary equation and find the value of the unknown;

Substituting the value of the obtained unknown into any one of the original equations to find the value of another unknown;

The value of two unknowns is the solution of the system of equations by "{";

Finally, check whether the results obtained are correct (substituted into the original equation system for testing, whether the equation satisfies the left = right).

For example: {5x+3y=9.}

10x+5y=12②

Enlarge it by 2 times

10x+6y=18

Get: 10x+6y-(10x+5y)=18-12

y=6 and bring y= intoor Medium.

Solution: {x=.}

y=6

To add, subtract, and eliminate an unknown is to eliminate an unknown. Like what.

x+y=52x-3y=5

To eliminate an unknown, make the coefficient in front of any unknown in x+y=5 the same as 2x-3y. Then there is.

2x+2y=10 (multiplying 2 on both sides is constant.) Next, since the coefficients in front of x are the same, then subtract the two sides of the equation 2x+2y=10 and 2x-3y=5 to get 5y=5, then y=1.

Then take y into the original formula and calculate x. Then x=4

Solution: x 2 + y 3 = 5, multiply x x 2 + y 3 = 5 by 9 to get it, add it to 2x-3y=-6, , and add it to get x=6, y=6

Addition, subtraction, and elimination are essentially the use of algebraic mergers to combine similar terms, and reduce the coefficients in front of an unknown number to 0, so as to obtain a unary equation.

Just make the coefficients of the same unknown the same, and then use addition and subtraction, e.g. x+y=5, x-y=3

The two formulas add and cancel y, and the two formulas subtract x

A system of binary linear equations, using algebraic methods.

Example: 3a+2b=4

a+2b=2②

by - 3a-a) + (2b-2b) = 4-22a = 2

a=1 brings a=1 into .

1+2b=2

2b=2-1

b=1／2

The coefficients of the same letter in the system of equations are converted into the same or opposite numbers, and then the binary system of linear equations is transformed into a univariate linear equation by adding or subtracting the elements.

: In two binary systems of one-dimensional equations, when the coefficients of the same unknown are equal and opposite, the two sides of the two equations can be subtracted or added respectively to eliminate the unknown and obtain a one-dimensional equation, which is called addition, subtraction, and elimination, or addition and subtraction.

Solve the system of equations {y=x-3 7x+5y=-9;{3x+5y=12 3x-15y=-6 The easiest way to do this is (c).

a.The substitution method is used.

b. All use the elimination method.

c Use the substitution method, use the elimination method.

d.Use the elimination method, use the substitution method.

The equation obtained by subtracting x from the system of equations {8x-3y=9 8x+4y=-5 is (b).

b.-7y=14

The system of equations {3x-2y=6 2x-5y=4 will give 2-3 (c).

The optimal solution for the system of equations {3x-y= 3x+2y=11 is ( c ).

a.Get y=3x-2 and bring it in

b.From 3x=11-2y, bring in

c.By - subtract x

d.By 2+, remove y

The solution of the system of equations {x+y=3 2x-y=6 is x=3, y=0

Knowing that x,y satisfies the system of equations {2x+y=5 x+2y=4, then the value of x-y is 1

The solution of the binary system of linear equations {x+y=2 2x-y=1 is (b).

a.{x=0 y=2

b.{x=1 y=1

c.{x=-1 y=-1

d.{x=2 y=0

If we know {3x=4+m,2y-m=5, then the relationship between x and y is ( c ).

The system of equations {x+y=5 ,2x+y=10 , and the correct system of equations obtained by - is (b).

Solving a system of equations by addition and subtraction {2x-3y=5 3x-2y=7 The following statement is incorrect (d).

a.3-2, remove x

b.2-3, remove y

c.3-2, remove x

d.2-3, remove y

If (x+y-5) is the same as |3y-2x+10|are opposites, then the value of x,y is (d).

y=2y=3

y=5y=0

The third question x+6y-2 + 3x-y+5=9 is sorted out: 4x+5y=6x+6y-2 -(3x-y+5)=9 is sorted out: 2x-7y=-16 The system of equations is solved: x= -1, y=2

Question 1: Speed = (60 divided by 3 + 60 divided by 2

Water velocity = (60 divided by 3-60 divided by 2

The second problem is 2x+y=7, then y=7-2x is substituted into the second equation to obtain.

x+2(7-2x)=8

3x=-6x=2, then y=7-4=3

Question 4: 2x+y=5

x-y=7②

Solution: +3x=12

x=4∴y=-3

In the fifth question, x=1 and y=2 are substituted into the system of equations, and we get: 2a-2b=3

a+2b=6

2a-2b=3 ①

2a+4b=12 ②

Obtained by - 6b=9

Solution; b=3/2 a=3

a+b=9/2

Question 6 x+2y=10 2x-y=5 The solution of these two systems of equations is .

x=4 y=3 This is the same solution of the two equations in the original problem, substituting ax+by=1 and bx+ay=6.

4a+3b=1

3a+4b=6 gives a=-2 b=3

Seventh solution: The unit price of apples in the store is X yuan per kilogram, and the unit price of pears is Y yuan per kilogram

Answer: The unit price of apples in the store is 5 yuan per kilogram, and the unit price of pears is 9 yuan per kilogram

Question 8: 3x-2y+1=0

2x+5y-12=0

x=1 y=2

4x-y+5/3x+2y

Be sure to adopt.