Question

$5x-2y=6$, $15x-6y=c$
Which of the following choices of $c$ will result in a system of linear equation with no solution?

• A. $c=18$
• B. $c$ can be any number other than $-18$
• C. $c$ can be any number other than 18
• D. $c$ can be any number

Answer 1

The correct option is C $c$ can be any number other than 18

Look at the equation very carefully $5x-2y=6$
$15x-6y=c$
Ratio of coefficient of $x=\frac{1}{3}$
Ratio of coefficient of $y=\frac{1}{3}$
So if ratio of constant become equal to $\frac{1}{3}$; ; then system will have infinitely many solutions, therefore, $\frac{6}{c}\ne \frac{1}{3}$
That means $c$ cannot be equal to 18. Correct answer is option C.