Respuesta :

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
frika

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

[tex]\dfrac{1}{2}=\dfrac{-3}{q}=\dfrac{4}{8}.[/tex]

Solve it:

[tex]\dfrac{1}{2}=\dfrac{-3}{q},\\ \\1\cdot q=-3\cdot 2,\\q=-6.[/tex]

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

[tex]\dfrac{1}{2}=\dfrac{-3}{-6}=\dfrac{4}{8}.[/tex]

Answer: q=-6.