Given that x = 2, y = 3, z = 1 is the solution of the equations ax + by + CZ = 4, ax by CZ = 4, ax by + CZ = 10, find the value of ABC

Given that x = 2, y = 3, z = 1 is the solution of the equations ax + by + CZ = 4, ax by CZ = 4, ax by + CZ = 10, find the value of ABC

Substitute XYZ into three equations respectively
The result is: 2A + 3B + C = 4
Formula 2a-3b-c = 4
Formula 2a-3b + C = 10
A = 2 is obtained by adding two forms to two forms, and B and C are obtained by three forms
2a+3b+c=4
2a-3b-c=4
2a-3b+c=10
A = 2 is the sum of the two forms
Subtract three from one to get b = - 1
Three minus two, C = 3
Ax + by = 2C ① (where a, B, C are constants and ABC ≠ 0) help to solve! CZ + AX = 2B ② by + CZ = CZ ③
x=2c/a; y=0; z=(2b-2c)/c.
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If the solution of ax-by-2z = 13 ax + 2Y + CZ = - 2 cx-4y + BZ = 28 is x = 3 y = - 1 z = - 2, find the value of ABC
The original equations of x = 3, y = - 1, z = - 2 generations are sorted out
3A+B=9①,
3A-2C=0②,
3C-2B=24③.
① - 2, B + 2C = 9, 4
At the same time, the solution is b = - 3, C = 6
The solution of C = 6 generation 2 is a = 4
∴ABC=4×（－3）×6=-72
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The original equations of x = 3, y = - 1, z = - 2 generations are sorted out
3A+B=9①，
3A-2C=0②，
3C-2B=24③.
① - 2, B + 2C = 9, 4
At the same time, the solution is b = - 3, C = 6
The solution of C = 6 generation 2 is a = 4
Take the values of X, y, Z and solve the equation. It's very simple
3A+B=9①
3A-2C=0②
3C-2B=24③
① - 2, B + 2C = 9, 4
③ The solution is b = - 3, C = 6
The solution of C = 6 generation 2 is a = 4
∴ABC=4×（－3）×6=-72
The original equations of x = 3, y = - 1, z = - 2 generations are sorted out
3A+B=9①，
3A-2C=0②，
3C-2B=24③.
① - 2, get
3a+b-3a+2c=9-0
b+2c=9 ④
③.+④*2
3C-2B+2(b+2c)=24+2*9
5c=42
C = 8 and 2 / 5
If the system of inequalities 2x-3 is greater than or equal to 0, x + 1 is less than or equal to m, there is no solution to find the value range of M
2x-3 greater than or equal to 0
X ≥ 3 / 2
X + 1 less than or equal to M
M-1 ≥ X
If there is no solution, then M-1 < 3 / 2
m< 5/2
2x-3≥0
x≥3/2
x+1≤m
x≤m-1
That is, 3 / 2 ≤ x ≤ M-1 has no solution
That is, 3 / 2 ≤ M-1 does not hold
So 3 / 2 > M-1
M3 / 2, and x < M-1
So M-1 "3 / 2"
m《5/2。
2x-3≥0 x≥1.5
x+1≥2.5
Then M < 2.5
2x-3>=0
x>=3/2
4-3x=(4-m)/3
Because the system of inequalities has no solution
So the value range of M is empty
2x-3 greater than or equal to 0
X is greater than or equal to two thirds
X + 1 less than or equal to M
X is less than or equal to M-1
Because the inequality has no solution
So M-1 is less than three-thirds
So m is less than 5 / 2
2x-3≧0 x≧3/2
x+1≦m x≦m-1
The system of inequalities has no solution
3/2>m-1
M
Y = 3x square + X + 3x ∈ r to find the range of Y
Preparation method --
The original equation can be reduced to y = 3 (x + 1 / 6) ^ 2 + 35 / 12
So the range of Y is [35 / 12, positive infinity]
If the system of inequalities XA-1 has no solution, then the range of a is————
2a+1≤a-1
a≤-2
The meaning of the title leads to 2A
Finding the square of y = x-3x + 4 to get the range
Y=X^2—3X+4
=(x-3/2)^2-9/4+4
=(x-3/2)^2+7/4≥7/4
So the square of y = x-3x + 4 has a range of [7 / 4, positive infinity]
The opening is upward, the subtraction of 4ac from B is less than 0, and there is no intersection between the image and x-axis
The minimum value is 7 / 4 at the vertex
The range is [7 / 4, positive infinity]
The range is [7 / 4, + ∞)
If x > A + 1 x
To make the inequality system x > A + 1 x
2a+1
The range of y = 1-3x, X ≤ - 1 or X ≥ 2
Y = 1-3x monotone decreasing
When x ≤ - 1, the minimum value f (- 1) = 1-3 * (- 1) = 4, range [4, + infinity]
When x ≥ 2, the maximum f (2) = 1-3 * 2 = - 4, range (- infinity, - 4]
If x > A, X
x>a,x