Homework test issues: Find value of n so system of equations has no solution

[Nicole.ss]

I learn system of equations.

6. Consider the following system of two linear equations.

$\qquad \qquad \begin{cases} x-2y &= 3 \\ nx+4y &= 6 \end{cases}$

Find the value of $n$ such that the system has no solutions.

I didn't figure it out, how to solve the system of equations when there is "n" with x or y.
It seems much harder than when "n" is after equation.

 

[Nicole.ss]

I get the answer is
-2
Is it right?

 

[MarkFL]

I get the answer is
-2
Is it right?

Yes, that is correct. Can you explain why it is correct?

 

[NotJeffM]

This is a tricky question.

In general, if you have u unknowns in linear equations, you need u equations to solve the system. So you are right that your ordinary methods will not work. Here you have three unknowns and only two equations. An exception to that general rule is that the system IS solvable if you have enough extra information. Here you know that n makes the system have no solution. That turns out to be enough extra information.

Think graphically: if a system of linear equations has no solutions, then the lines representing those equations do not intersect. Therefore, they are parallel. Can you answer Mark’s question with this hint?

 

[Nicole.ss]

Oh thank you NotJeffM for the explenation.
I don't really remember how I solved it as it was a few days ago, but yes I used the info that systems has no solution.

Thank you mark also ^^