Answer:
[tex]\left \{ {{3x+3y=0} \atop {7x-y=8}} \right.[/tex]
Step-by-step explanation:
An equivalent system refer to other system that has the same values for the variables, or it's satisfied by the same values. First, we calculate what are the values for x and y, in the given system.
[tex]\left \{ {{3x+3y=0} \atop {-4x+4y=-8}} \right.[/tex]
Extracting common factors:
[tex]\left \{ {{3(x+y)=0} \atop {4(-x+y)=-8}} \right. \\\left \{ {{x+y=0} \atop {-x+y=-2}} \right.[/tex]
Now, summing both equations we have:
[tex]2y=-2\\y=-1[/tex]
Replacing this value in a equation we have:
[tex]3x+3y=0\\3x+3(-1)=0\\3x-3=0\\x=\frac{3}{3}=1[/tex]
Now, we have to find the other system that it's satisfied by [tex]y=-1[/tex] and [tex]1[/tex].
[tex]\left \{ {{3x+3y=0} \atop {7x-y=8}} \right.\\3(1)+3(-1)=0\\3-3=0\\0=0\\7(1)-(-1)=8\\7+1=8\\8=8[/tex]
As you can see, the first system is equivalent because it has the same solution as the given system of equations.
Therefore, the correct answer is the first one.
