x+y+4z-4=0,2x+3y+6z-5=0,2y+z-3x+4=0 D=23,Dx=23 Dy= -23 ,Dz=23 then y=
Answers
The value of y = -1
Given:
x + y + 4z - 4 = 0
2x + 3y + 6z - 5 = 0
2y + z - 3x + 4 = 0
D = 23
Dx = 23
Dy = -23
Dz = 23
To find:
The value of y
Solution:
you can use Cramer's rule, which states that if the determinant of a system of equations is non-zero, the value of each variable can be found by taking the determinant of the system with the constant term replaced by the corresponding column vector, and dividing by the determinant of the original system.
In this case, the determinant of the original system (D) is 23, the determinant of the system with the constant term in the x column replaced by the column vector (-23) is Dx, the determinant of the system with the constant term in the y column replaced by the column vector (-23) is Dy, and the determinant of the system with the constant term in the z column replaced by the column vector (23) is Dz.
Using Cramer's rule, the value of y can be found by:
y = Dy / D
Substituting the given values into this equation gives:
y = (-23) / 23
Which simplifies to:
y = -1
Therefore, the value of y in the system of equations is -1
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Answer: Y = -1 is the answer to the above given question.
Step-by-step explanation: Given
x + y + 4z - 4 = 0
2x + 3y + 6z - 5 = 0
2y + z - 3x + 4 = 0
D = 23
Dₓ = 23
Dy = -23
Dz = 23
we have to find the value of y
To calculate the value of y let us use cramer's rule
Cramer's Rule Formula :
Consider a linear equation with n variables written in a matrix form as AX = B
Where A = coefficient matrix,
B = column matrix with constants and
X = column matrix with variables
Now to find determinants as
D = | A | , Dₓ₁, ........ Dₓₙ
D is the determinant
Thus,
X₁ = Dₓ₁ ÷ D
X₂ = D ₓ₂ ÷ D
D ≠ 0
By using this cramer's rule y value can be calculated as follows
Given D = 23
Dy = -23
Y =
Y =
Y = -1
Here are two links provided to know how cramer's rule is applied in few examples.
https://brainly.in/question/3479853
https://brainly.in/question/17294686
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