By using Cramer's rule we get the solution of the the given system of equations as x=23/32 and y = 21/32
Why do we use Cramer's rule in matrices?
One of the key techniques used to solve an equation system is Cramer's rule. The determinants of matrices are used in this method to derive the values of the system's variables. Thus, the determinant technique is another name for Cramer's rule.
Given, the linear system of equations is:
2x+6y=3
-5x+y=4
This is in the form of ax₁ ₊ by₁ = c₁ and ax₂ ₊ by₂ = c₂
Now we find the determinant of matrix A:
A = [2 6]
[₋5 1]
A = 2 ×1 ₋ 6 × (₋5) = 2 ₋ (₋30)
A = 32
Determinant of matrix B
B = [2 3]
[₋5 4]
B = 2×4 3×(₋5) = 8 ₋ (₋15)
B = 23
Now find the determinant Dx
Dx = [6 3]
[1 4]
Dx = 6×4 ₋ 3×1 = 24 ₋ 3
Dx = 21
Now we find the values of x and y.
Therefore , x = Determinant of B/ Determinant of Dx
x = 23/32
y = Determinant of A/ Determinant of Dx
y = 21/32
Hence we get the solution of the equation as x=23/32 and y = 21/32
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