Question

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

$4x+8y=5$ and $3x+6y=7$

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

Answer 1

The correct option is A no solution

Given, $4x+8y=5$, $3x+6y=7$

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

$D=\left|\begin{array}{cc}4& 8\\ 3& 6\end{array}\right|=4\times 6-3\times 8$

$D=24-24=0$

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

$D_x=\left|\begin{array}{cc}5& 8\\ 7& 6\end{array}\right|=5\times 6-8\times 7$

$D_x=3056=-26$

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

$D_y=\left|\begin{array}{cc}4& 3\\ 5& 7\end{array}\right|=4\times 7-5\times 3$

$D_y=2815=13$

Therefore, $D=0,D_x=-26\ne 0,D_y=13\ne 0$ the equation has no solution.