Verified Answer :

1) First eqation
x-3y=4

2) 2x+qy=8

It looks like if first equations is multiplied by 2 we get second equation, So let do it
2x-6y=8

So we see that in place of q is -6

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If the solution of the system is  {(x,y) : x-3y=4}, then both equation should have proportional coefficients:

\(\dfrac{1}{2}=\dfrac{-3}{q}=\dfrac{4}{8}.\)

Solve it:

\(\dfrac{1}{2}=\dfrac{-3}{q},\\ \\1\cdot q=-3\cdot 2,\\q=-6.\)

Check whether q=-6 is correct answer, substituting this value into the first ratio:

\(\dfrac{1}{2}=\dfrac{-3}{-6}=\dfrac{4}{8}.\)

Answer: q=-6.

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