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Question

Find the number of solutions for the equation using Cramer's rule.:

3x+4y=1 and 9x+12y=3

A
no solution
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B
infinite solution
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C
many solution
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D
two solution
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Solution

The correct option is B infinite solution
Given equations are 3x+4y=1,9x+12y=3

Using Cramer's rule, find the determinant of the coefficient matrix,

D=34912=3×124×9

D=3636=0


Secondly, find the determinant of x coefficient matrix,

Dx=14312=1×123×4

Dx=1212=0

Similarly, find the determinant of y coefficient matrix,

Dy=3193=3×39×1

Dy=99=0

Applying Cramer's rule, we have

x=DxD

x=00=0

y=DyD

y=00=0

Therefore, D=0,Dx=0,Dy=0 the equation has an infinite solution.


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