Question

solve by creamers rule find the value of x, y, z,

xy+yz+zx=xyz

2xy+3yz+zx =4xyz

4xy+9yz+zx=16xyz​

Answer 1

Answer:

The system is:

xy + yz + zx = xyz

2xy+3yz+zx=4xyz

4xy+9yz+zx=16xyz

Divide all equations by xyz. This gives:

(1/x) + (1/y) + (1/z) = 1

3(1/x) + (1/y) + 2(1/z) = 4

9(1/x) + (1/y) + 4(1/z) = 16

Let a = 1/x, b = 1/y, c = 1/z. Hence:

a + b + c = 1

3a + b + 2c = 4

9a + b + 4c = 16

This is a system of linear equations. You can now use your Cramers' rule at this point. Now:

D = 2

D_a = 6

D_b = 2

D_c = -6

Hence:

a = D_a/D = 3

b = D_b/D = 1

c = D_c/D = -3

Finally:

x = 1/3

y = 1

z = -1/3

Answer 2

Answer:

The system is:

xy + yz + zx = xyz

2xy+3yz+zx=4xyz

4xy+9yz+zx=16xyz

Divide all equations by xyz. This gives:

(1/x) + (1/y) + (1/z) = 1

3(1/x) + (1/y) + 2(1/z) = 4

9(1/x) + (1/y) + 4(1/z) = 16

Let a = 1/x, b = 1/y, c = 1/z. Hence:

a + b + c = 1

3a + b + 2c = 4

9a + b + 4c = 16

This is a system of linear equations. You can now use your Cramers' rule at this point. Now:

D = 2

D_a = 6

D_b = 2

D_c = -6

Hence:

a = D_a/D = 3

b = D_b/D = 1

c = D_c/D = -3

Finally:

x = 1/3

y = 1

z = -1/3

Step-by-step explanation:

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