Question

Solve the equations x+2y+3z=6,2x+4y+z=7,3x+2y+9z=14 using crammers rule

Answer 1

# Answer- (x,y,z)=(1,1,1)

# Solution-

Given equations:

x+2y+3z=6,

2x+4y+z=7,

3x+2y+9z=14.

Cramers rule states determinants are used to solve the system of linear equations.

Find determinant D

1 2 3
2 4 1 =D
3 2 9

D=2[(1)(18-1)-(1)(18-3)+3(2-6)]

D=2[17-15-12]

D=-20

Find D1

6 2 3
7 4 1 =D1
14 2 9

D1=-20

Find D2

1 6 3
2 7 1 =D2
3 14 9

D2=-20

Find D3

1 2 6
2 4 7 =D3
3 2 14

D3=-20

The derterminant is non-zero number means the system has unique solution.

The solution of these equation is,

x=D1/D=-20/-20=1

y=D1/D=-20/-20=1

z=D1/D=-20/-20=1

(x,y,z)=(1,1,1)