Question

Solve the following equations using Cramer's rule.
x + 2 y + 3 z = 6, 2 x +4 y + z = 7, 3 x, 2 y + 9 z= 14​

Answer 1

Answer:# 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

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