A and B solved the equations MX + y = 5 ①, 2x NY = 15 ② at the same time. When a was solving the problem, he misread m in ① and got x = 4, y = - 7; while B was wrong about N in ②, he got x = 2, y = 3

A and B solved the equations MX + y = 5 ①, 2x NY = 15 ② at the same time. When a was solving the problem, he misread m in ① and got x = 4, y = - 7; while B was wrong about N in ②, he got x = 2, y = 3

Generation X = 4; y = - 7 into ②
8+7n=15
N=1
2; X = 2
2m+3=5
M=1
If M = 1 and N = 1, then
x+y=5③
x-y=15④
③+④
2x=20
x=10
Generation X = 10 in ③
10+y=5
y=-5
That is, the solution of the original equations is x = 10; y = - 5

Simultaneous solution of equations by two persons a and B mx+ny＝−8(1) MX − NY = 5 (2), because a misread m in equation (1), the solution is x＝4 Y = 2, B misread n of (2) in the equation, and the solution is x＝2 Y = 5, try to find the correct value of M, n

A misread m in equation (1), and the solution is
x＝4
Y = 2, so 4m-2n = 5,
B misread n in equation (2), and the solution is
x＝2
Y = 5, so 2m + 5N = - 8,
By solving the equations, we get
m＝3
Eight
n＝−7
4 ．

Simultaneous solution of equations by two persons a and B mx+ny＝−8(1) MX − NY = 5 (2), because a misread m in equation (1), the solution is x＝4 Y = 2, B misread n of (2) in the equation, and the solution is x＝2 Y = 5, try to find the correct value of M, n

A misread m in equation (1), and the solution is
x＝4
Y = 2, so 4m-2n = 5,
B misread n in equation (2), and the solution is
x＝2
Y = 5, so 2m + 5N = - 8,
By solving the equations, we get
m＝3
Eight
n＝−7
4 ．

On the two systems of equations of XY, 2x-y = 0, the two equations of XY {2x-y = 0 2x + y = m and {X-Y = 5 2x-y = n-1) have the same solution

It's very simple. You combine 2x-y = 0 and X-Y = 5

It is known that the system of equations {2x + 3Y = - 5,3x + 7Y = m for X, Y. when - 18 < m ＜ - 10, there is an integer solution, x ^ 2 + XY + y ^ 2=

By solving the equations
5y=2m+15
y=2m/5+3
When - 18 ＜ m ＜ - 10, there is an integer solution
So m = - 15
Therefore, x = 2, y = - 3
x^2+xy+y^2=4-6+9=7

If the solution of the system of equations 2x + y = 1-m x + 2Y = 2 for XY satisfies x + Y > 0, then the value range of M is

I don't know what method you will use, but I use the method of coefficient matrix, which is very simple
Can find: x = - (2m) / 3;
y=(3+m)/3
X + Y > 0 is required, that is, x > - Y;
-（2m）/3 > (3+m)/3
We can get: M

Given that the solution XY of the system of equations {2x-y = 4m + 3,2y-x = - 3 is opposite to each other, find the value of M

On the contrary, y = - X
So 2y-x = - 2x-x = - 3
-3x=-3
x=1,y=-1
Substituting 2x-y = 4m + 3
2+1=4m+3
M=0

Given the solution x, y of the system of equations 2x-y = 2 + 3M [1] x + 2Y = 1-m [2], the value range of M is obtained

(1) * 2 + (2) gives 5x = 4 + 6m + 1-m and x = m + 1,
Substituting (1) gives y = - M,
It is known that - M (M + 1) > 0,
So m (M + 1)

On the two equations of X, y (2m + n) X-my = 9; X + y = 5 and MX + NY = 13:2x-y = 4 have related solutions

That is, the four equations have the same solution
x+y=5
2x-y=4
Add up
3x=9
X=3
y=2x-4=2
Put in the other two
3(2m+n)-2m=9
3m+2n=13
Namely
4m+3n=9
3m+2n=13
m=21,n=-25

It is known that the solution of the system of equations about XY 2x-3y = m x-ny = 2 is x = 2Y = 3. Find the value of the algebraic expression 2m + 3N

From x = 2Y = 3
Know equation system
2x-3y=m
x-ny=2
The solution of is
x=3,y=3/2
Back to the equations, we get
2*3-3*3/2=3/2=m
3－3/2*n＝2
have to
m=3/2,n=2/3
therefore
2m+3n＝2*3/2+3*2/3=3+2=5