Question

$-x=-7y-8$ , $x-7y=k$
Consider the system of equations above. Which of the following choices of $k$ will result in a system of equations will infinitely many solutions?

• A. Any number
• B. Any number except 8
• C. 8
• D. $-8$

Answer 1

The correct option is C 8

Lets rewrite the equation $x-7y=8$
$x-7y=k$
For infinitely many solutions, ratio of coefficient of $x=$ ratio of coefficient of $y=$ ratio of constant.
Therefore $k=8$
If $k=8$, the system will have infinitely many solutions.