x 2y 7k 3 x 4y k 3 binary linear equation to solve the problem in detail

x+2y=7k+3 ①

x-4y=k-3 ②

Solution 1: Elimination method.

6y=6k+6, and the solution is y=k+1

3x=15k+3, and x=5k+1

x=5k+1，y=k+1

Solution 2: Substitution method.

From: x=4y+k-3, substitution

4y+k-3+2y=7k+3

6y=6k+6

y=k+1, substitution

x=4(k+1)+k-3=5k+1

x=5k+1，y=k+1

Solution 3: Elimination method + substitution method.

6y=6k+6, the solution is y=k+1, substitution

x=4y+k-3=4(k+1)+k-3=4k+4+k-3=5k+1

x=5k+1，y=k+1

Solution: 1. The conventional solutions to binary equations include elimination method and substitution method. Three different solutions are given above, all of which are effective solutions for solving such equations.

2. The first solution method is the elimination method, which is suitable for binary systems of equations that are easy to observe by the least common multiple of the unknown number coefficient;

The second solution method is the substitution method, which is relatively computationally large, and is suitable for binary linear equations that are not easy to be directly observed by the least common multiple of unknowns.

The third solution is to combine the advantages of the two solutions, in the solution step, the elimination element is used when the elimination element is used, and the substitution is used when it is applicable, which is more flexible.

x+2y=7k+3 (1)

x-4y=k-3 (2)

1)-(2) 6y=6k+6 => y=k+1 substituting y=k+1 into (1) gives x+2*(k+1)=7k+3 => x+2k+2=7k+3 => x=5k+1

The solution of the system of equations is x=5k+1, y=k+1

The two solutions of the equation are equal.

Missed feast x=y

4x+3x=7

x=y=1

The substitute party returns to pure Chengde.

k+k-1=3

2k = 4 to get k = 2

3x+4y=2k-3 --1)

2x-y=3k+4 --2)

1)+(2)*4.

11x=14k+13

x=(14k+13) 11 substitution (2)y=-(19k+31) 11

and x+y=2

14k+13) 11-(19k+31) pila 11=2 then type grip tremor k=-8

x=-9y=11

1) 2x+3y=k (3 on both sides).

3）6x+9y=3k

2) 3x+4y=2k+6 (2 on both sides).

6x+8y=2(2k+6)=4k+12 subtracted from (3))6x+9y=3k

y=3k-4k-12

y=-k-12 (substituted to (1).)

2x+3(-k-12)=k

2x-3k-36=k

2x=k+3k+36

2x=4k+36

x=2k+18

It is also known that x+y=3

2k+18+(-k-12)=3

2k+18-k-12=3

k=-3x=2k+18=2*(-3)+18=12y=-k-12=-(3)-12=-9 check: