Find the number of solutions for the equation using Cramer's rule.:
Using Cramer's rule, find the determinant of the coefficient matrix,
D=∣∣∣34912∣∣∣=3×12−4×9
D=36−36=0
Secondly, find the determinant of x coefficient matrix,
Dx=∣∣∣14312∣∣∣=1×12−3×4
Dx=1212=0
Similarly, find the determinant of y coefficient matrix,
Dy=∣∣∣3193∣∣∣=3×3−9×1
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.