Question

In the system of equations above, $a$ is a constant. For $-3x+y=6;ax+2y=4$
Which of the following values of $a$ does the system have no solution?

• A. $-6$
• B. $-3$
• C. $3$
• D. $6$

Answer 1

The correct option is A

$-6$

Explanation for the correct option:

No solution condition of lines:

Given system of equation is

$-3x+y=6;ax+2y=4$.

The system has no solution if the lines represented by these equations are parallel.

And the two lines are parallel if their slopes are equal.

Consider slope intercep form of line, $y=mx+c$.

For equation $-3x+y=6$,

$slope=m=3$

For equation $ax+2y=4$,

$slope=m=\frac{-a}{2}$

$\begin{array}{rcl}\Rightarrow 3& =& \frac{-a}{2}\\ & \Rightarrow & -a=6\\ \Rightarrow a& =& -6\end{array}$

Therefore, the correct answer is option (A)