Hello!
First, let's rewrite the system as a matrix:
Let me explain:
• 1st, column: coefficients from x
,
• 2nd, column: coefficients from y
,
• 3rd ,column: coefficients from z
,
• 4th, column: results
Now, we must calculate the determinant of the matrix 3x3 of the values of x, y, z, look:
To calculate the determinant of a matrix, we will multiply all values of the main diagonal and subtract the secondary diagonal from it.
Let me explain in more detail in a drawing:
Now, let's calculate three more determinants. This time, we will remove the column of the variable that we are working with and replace it with the column of the results, look:
To calculate the values of x, y and z, we have to divide the determinant of the variable by the determinant of the initial matrix, look:
Answer:
(x, y, z) = (2, -1, 1)
X = 2
Y = -1
Z = 1