Question

For what value of "$c$" will the equations $3x-4y=7$ and $x+cy=13$ have no solution?

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

Answer 1

The correct option is D $\frac{-4}{3}$

A system of two linear equations has no solution when the lines are parallel.

$3x–4y=7$

$\Rightarrow$ $4y=3x-7$

$y=\frac{3}{4}x–\frac{7}{4}$

$\therefore m_1=\frac{3}{4}$

$x+cy=13$

$\Rightarrow$ $cy=13-x$

$y=-\frac{1}{c}x+\frac{13}{c}$

$\therefore m_2=-\frac{1}{c}$

Parallel lines have the same slope-

$\therefore m_1=m_2$

$\Rightarrow \frac{3}{4}=-\frac{1}{c}$

$\Rightarrow c=\frac{-4}{3}$

Hence, for $c=\frac{-4}{3}$, the given system of equations will have no solution.