Binary Equation Addition, Subtraction, and Elimination There are a few questions that won t!

The following 5 sets of equations, two of which are numbered separately

1。*2+ *3=(2*2+3*3)x=6*2-2*3【Elimination】 13x=6,x=6 13, substituting or getting y=22 13

The same is true for the following.

2。*3+ = elimination y

3。*3+ = elimination y

4。*4- *3 = elimination y

5。*2+ *3=eliminate y

Tip: Observe the coefficients of x and y of 2 equations respectively.

1. If there is a multiple relationship, such as the coefficient of y in question 2, -1 and 3. Then *3, which is added to cancel out y.

2. If there is no multiplier relationship, such as the first question, select an unknown number to be eliminated, such as y, the coefficients are 3, -2 respectively, find the least common multiple (regardless of plus or minus), which is 6, then multiply by 2 (6 3), multiply by 3 (6 2). In this case, the sum of the coefficients of y is zero, then the two equations are added (if the difference is zero, then subtracted).

Got it? If you practice more, you'll become proficient.

The first question, 1 formula * 2 + 2 formula * 3 = , the second question 1 formula * 3 + 2 formula = , three questions, 1 formula + 2 formula * 3 = , four questions, 1 formula * 3-2 formula * 4 =, five questions, 1 formula * 2 + 2 formula * 3 = can only teach you the method to calculate the result yourself, this kind of problem can eliminate an unknown number by increasing the multiple of the two formulas to add and subtract.

This uses the elimination method, the first question x=8 13 y=22 13 the second question x=3 y=1 the third question x=1 y=2 the fourth question x=-10 7 y=25 7 the fifth question x=2 y=-1

The solution method of binary linear equation is as follows:

1. When the coefficients of the same unknown in the two equations of the binary linear equation system are opposite to each other or equal, the two sides of the two equations are added or subtracted respectively to eliminate the unknown number and obtain a unary equation, which is called the addition and subtraction method, referred to as addition and subtraction.

2. General steps for solving binary linear equations by addition and subtraction:

1) Transformation coefficient: Multiply an equation or both sides of two equations by the appropriate number, so that the coefficient of an unknown number in the two equations is opposite to each other or equal.

2) Addition, subtraction, and elimination: add or subtract both sides of two equations respectively, and subtract an unknown number to obtain a unary one-dimensional equation.

3) Solve this unary equation to find the value of an unknown.

4) Retrogressive solving: substitute the value of the unknown into any equation of the original equation system to find the value of another unknown in the slag segment.

5) Write the solution of this system of equations in the form {x=ay=b).

Addition, subtraction, and elimination method: 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.

Steps. Using the basic properties of the equation, the coefficients of an unknown number in the original equation cave group are 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).

1) Subtract the second equation from the first equation to obtain: (3x-3x)+2y-(-2y)=9-3

4y=6y=6/4

Approximation. y=3/2

Substitute y=3 2 into 3x-2y=3.

3x-2*3/2=3

3x=6x=2

2) Add the first equation to the second equation to obtain: (6x+3x)+(4y+4y)=37-4

9x=33x=33/9

Put x=33 9

Substitute 3x+4y=-4.

4y=-15

y=-15/4

3) Put 6m-3n = 15

Divide by 3 on both sides

Get: 2m-n=5

Then multiply 2m-n=5 by 8 on both sides to get :

16m-8n=40

Put 9m + 8n = 10

with 16m-8n = 40

Summing: (9m+16m)+(8n-8n)=40+1025m=50

m=2 is substituted into 2m-n=5.

4-n=5n=-1

4) Add the two equations to obtain: (x-3) 2+(x-3) 2+ (y-2) 3-(y-2) 3 =6

x-3+x-3)/2=6

Multiply the dust on both sides by 2

2x-6=12

2x=18x=9

Substitute x=9.

x-3)/2+(y-2)/3=4

3+(y-2)/3=4

y-2)/3=1

y-2=3y=5

I've been fighting for a long time! (Hopefully, it will work for you!) ~

2x+5y=15

3x+8y=-1

Multiply the two sides of the first equation by 3: 6x+15y=45

The second equation is multiplied by 2 on both sides: 6x+16y=-2 (that is, let the coefficient of x be judged by the cherry blossoms, etc., so look for the least common multiple to change the number of rounds, so as to eliminate x).

Subtract the two equations y=-47

x=125

×3 9x+3y=-3 ③

Hail - 8x=-8

x=-1 put the x=-1 generation source formwork beam into y=2

x=-1

y=2 original=-1-2=-3

x+y=20 x+2y=25, the first one expands by 2, becomes 2x+2y=40, 40-25=2x-x, x=15

(1) Today, there are three cows and two sheep for a total of 1,900 yuan, and a cow and five sheep for a total of 850 yuan.

2) Put a number of chickens into a number of chicken cages, if each chicken cage is placed 4, there is a chicken without a cage; If there are 5 chickens in each cage, there is a cage without chickens, so how many chickens are there? How many chicken coops are there?

2x-5y=-21 ①

4x+3y=23 ②

x2 gives 4x-10y=-42

4x-10y-(4x+3y)=-42-23y=5, bring y=5 in

Find x=24x+7y=-19

4x-5y=17 ②

7y+5y=-19-17

y=-3 brings in to get.

x=5（y-1）=3）x+5

3x-3=y+5① 3x-y=8 ③

5y-5=3x+5② 3x-5y=-10④4y=18y=9/2

Bring in x=25 6

2（x-y)/3+y=5①

3(x-y) 2-5y shirt Hu dou 2=-3

Organize them separately.

2x+y=15③

3x-8y=-6 or grind.

8+ gotta be buried.

19x=114

Then x=6 substitutes x=6 into it.

y=3, then x=6y=3

2x+5y=15

3x+8y=-1

Multiply the two sides of the first equation by 3: 6x+15y=45

The second equation is multiplied by 2 on both sides: 6x+16y=-2 (that is, let the coefficient of x be judged by the cherry blossoms, etc., so look for the least common multiple to change the number of rounds, so as to eliminate x).

Subtract the two equations y=-47

x=125