Math problems about binary linear equations of addition and subtraction

1. 5x+2y=17①

3x-5=4y ②

Multiply by 2 to get.

10x+4y=34 , get. 13x=39

x=3 substituting x=3 into , we get 15+2y=17y=12 3x-2y=-7①

2x+5y=8②

x2, we get 6x-4y=-14

x3, get 6x+15y=24, get. 19y=38

y=2 substituting y=2 into , resulting in 2x+10=8

2x=-2x=-1

3. 2y+8=x①

4x+2y=11 , get. 4x-8=11-x

5x=19x=19/5

Substitute x=19 5 into , and get.

2y+8=19/5

2y=19/5-8

2y=-21/5

y=-21/10

4. 7x-13y=25①

9x-15=17y②

Multiply by 9 to get 63x-117y=225

Multiply by 7 to get 63x-105 = 119y, get. 105+117y=119y-2252y=-120

y=60 substitute y=60 into to get.

7x-780=25

7x=805

x=115

General steps for solving a system of binary equations by addition and subtraction: In two equations of a system of equations, if the coefficients of the same unknown number are neither equal nor opposite to each other, multiply the two sides of the equation with the appropriate number so that the coefficients of an unknown number are equal or opposite to each other Subtract or add the two sides of the two equations respectively to eliminate an unknown number to obtain a unary equation Solve this unary equation to find the value of the unknown Substitute the value of the unknown into any one of the equations of the original system of equations, Find the value of another unknown Write the value of the two unknowns together to get the solution of the original system of equations.

x=ay=b

formal representation

Example: Solving a system of equations:

x−y＝3①

2x y 12 to get 3x 15, solve x 5, substitute x 5 into , solve y 2, the solution of the original equation is.

x＝5y＝2

Solution: {x+y=18.}

By the way. Substitution.

Substitution. 30%x+75%y=50%x18②

x=18-y③

y=8x=10

If I'm not mistaken, you're taking the math problem on page 108 of the Song Wheel Scholar Teaching Song Edition, page 108).

Hit x two-pointers and Y free throws.

3*2+x*2+y=22

2+x+y=14

x=4 y=8

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?

×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

1) Let the number of people making shirts be x the number of people making pants and the number of people making pants be y

From x+y=24 3x=5y, we can calculate y=9 x=15(2), and let the number of people making shirts be x and the number of people making pants is y

From x+y=24 3*30x+5*16y, greater than or equal to 2100, x is greater than or equal to 18

So arrange at least 18 people to make the shirts.

(1) Set x workers to make shirts, (24-x) people to make pants, then 3x=5 (24-x) solution x=15

2) If y workers make shirts, and (24-y) people make pants, then 3 30y+5 16 (24-y)=2100 will get y=18

It should be the solution of a system of binary equations.

Commonly used are substitution elimination method and addition and subtraction elimination method.

For example, the system of equations 2x+y=10

x+3y=15②

By 2- the unknown x can be eliminated