It is known that the solution of {4mx-x + y = 13 2x-ny + 1 = 2 is {x = 2, y = - 1, then 2m + 3N =?

It is known that the solution of {4mx-x + y = 13 2x-ny + 1 = 2 is {x = 2, y = - 1, then 2m + 3N =?

x=2,y=-1
Substitution
8m-2-1=13
M=2
4+n+1=2
n=-3
So 2m + 3N
=4-9
=-5

It is satisfied that the value of Y in the system of equations 2x-y-4m = 0 14x-3y = 20 is 3 times of X. find the value of M and the value of XY / x + y

Y = 3x is substituted into the original equations
2x- 3x -4m =0 (1)
14x - 9x = 20(2)
By (2)
5x = 20
x = 4
Insert into (1)
-4 - 4m =0
m =-1
xy/(x+y) = 3x^2 / 4x = 3x/4 = 3
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1. If the solutions of the equations 4x-3y = 14, MX - (M + 4) y = 4 are opposite numbers to each other, then M=_________

XY is opposite to each other
4x-3y = 14 changes
4X+3X=14
X=2
Y=-2
Bring in
2M-(M+4)-2=4
2M+2M-8=4
4M=12
M=3

The solutions of the equations {x-2y = 0 MX + 2ny = - 4} {MX NY = 8 2x + 3Y = 14} are the same, and M is the value of Y

The key of this problem lies in elimination, and it is the same solution problem of two equations containing unknowns. Our idea is to use the unknown number to represent the solution of the first equation system, replace it into the second equation system, eliminate variables, and become an unknown equation, so it is easy to solve. The specific steps are as follows: 1

Given the equation system {2x-3y = 7 2mx-ny = 5. The solution is the same as that of {4x + y = - 7 MX + 2ny = - 20

2x-3y = 7 and 4x + y = - 7
x=-1 y=-3
Substituting x = - 1, y = - 3 into 2mx NY = 5 and MX + 2ny = - 20, we get the result
-2m+3n=5 -m-6n=-20
Solving equations
m=2 n=3

It is known that the values of X and y of the equation (2x + 3y-4) 2 + | x + 3y-7 = 0 are also about the solutions of the equations {MX + NY = 4; NX + my = 2 With the whole substitution method solution, must use the whole substitution method solution

∵(2x+3y-4)²+|x+3y-7|=0
∴2x+3y-4=0 x+3y-7=0
∴x=-3 y=10/3
The values of ∵ X and y are also related to the solutions of {MX + NY = 4; NX + my = 2
∴-3m+10/3n=4 10/3m-3n=2
The sum of the two formulas shows that M + n = 18

When m is the value, the solution of the equation system {x-5y = 2m {2x + 3Y = M-12 is opposite to each other?

x-5y=2m ,2x+3y=m-12
Replace x = 2m + 5Y into 2x + 3Y = M-12
Y = - (3m + 12) / 13
∴x=(11m-60)/13
∵x+y=(8m-72)/13=0
∴m=9
When m is 9, the solutions of the equations {x-5y = 2m {2x + 3Y = M-12 are opposite numbers

Equations 3x+5y＝k+2 2X + 3Y = K. if the values of X and y are opposite to each other, then the value of K is () A. 0 B. 2 C. 4 D. 6

By solving the equation, the following results are obtained
x＝2k−6
y＝4−k
According to the meaning of the title: (2k-6) + (4-K) = 0
The solution is: k = 2
Therefore, B

When m is the value, the solutions of the equations x = 5Y = 2m, 2x = 3Y = M-12 are opposite numbers to each other?

It should be: x-5y = 2m, 2x + 3Y = M-12?
Because X and y are opposite numbers to each other
Therefore, y = - x, substituting into:
So x + 5x = 2m, 2x-3x = M-12
The solution is: x = m / 3, x = 12-m
So, M / 3 = 12-m
The solution is: M = 9

When a is taken, the solutions of the equations 5x-3y = - 4A ① x + 5Y = a + 2 ② are opposite to each other, and the solutions of the equations are obtained When a is taken, the equation system {5x-3y = - 4A ① The solutions of {x + 5Y = a + 2) are opposite to each other, and the solutions of the equations are obtained

5x-3y=-4a
x+5y=a+2
The solutions are opposite to each other
So x = - Y
Get by substitution
-5y-3y=-4a
-y+5y=a+2
a=2y
a+2=4y
So 2Y + 2 = 4Y
Y=1
x=-y=-1
a=2y=2