Question

$\{\begin{array}{c}\frac{3}{4}x-\frac{1}{2}y=12\\ \\ kx-2y=22\end{array}$
If the above system of equations has no solution, find the value of $k$.

• A. $-\frac{4}{3}$
• B. $-\frac{3}{4}$
• C. $3$
• D. $4$

Answer 1

Answer: (C)

$3$

Given: $\frac{3}{4}x-\frac{1}{2}y-12=0$ and $kx-2y-22=0$

$\therefore a_1=\frac{3}{4},b_1=-\frac{1}{2},c_1=-12$

And, $a_2=k,b_2=-2,c_2=-22$

Since the given system of equations has no solution,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

$\frac{3}{4k}=\frac{1}{4}\ne \frac{12}{22}$

Hence, $k=3$