Question

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

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

• A. no solution
• B. infinite solution
• C. many solution
• D. two solution

Answer 1

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,

$D=\left|\begin{array}{cc}3& 4\\ 9& 12\end{array}\right|=3\times 12-4\times 9$

$D=36-36=0$

Secondly, find the determinant of $x$ coefficient matrix,

$D_x=\left|\begin{array}{cc}1& 4\\ 3& 12\end{array}\right|=1\times 12-3\times 4$

$D_x=1212=0$

Similarly, find the determinant of $y$ coefficient matrix,

$D_y=\left|\begin{array}{cc}3& 1\\ 9& 3\end{array}\right|=3\times 3-9\times 1$

$D_y=99=0$

Applying Cramer's rule, we have

$x=\frac{D_x}{D}$

$\therefore x=\frac{0}{0}=0$

$y=\frac{D_y}{D}$

$\therefore y=\frac{0}{0}=0$

Therefore, $D=0,D_x=0,D_y=0$ the equation has an infinite solution.