Use Cramers rule to solve the system x y z 3 x y 2z 10

Use Cramer\'s rule to solve the system. x + y - z = -3 x - y + 2z = 10 x + 5y - z = -23 Find the determinants. |A| =, |D_x| =, |D_y| =, |D_z| = The solution is x =, y =, and z =. (Type integers or simplified fractions.)

Solution

Your matrix

Write down the main matrix and find its determinant

D = -12

Replace the 1st column of the main matrix with the solution vector and find its determinant

Dx = -36

Replace the 2nd column of the main matrix with the solution vector and find its determinant

Dy = 60

Replace the 3rd column of the main matrix with the solution vector and find its determinant

Dz = -12

x = Dx / D = (-36) / (-12) = 3

y = Dy / D = 60 / (-12) = -5

z = Dz / D = (-12) / (-12) = 1

	X1	X2	X3	b
1	1	1	-1	-3
2	1	-1	2	10
3	1	5	-1	-23