The lines whose equations are 2x + y = 3z and x + y = 6z intersect at which point? (3z, -3z) (-3z, 9z) (9z, -15z)

Hey there, Xs4etsmith!

The correct answer would be the second option.
To solve for this system of equation, we need to make both equations equal to each other but first we need to make each equation equal to 0.

So,  goes to  (I subtracted  from both sides)
And  goes to  (I subtracted  from both sides)
Now we can make them equal to each other.

 (I subtracted y from both sides to cancel it)
 (I subtracted x from both sides)
 (I added 3z to both sides to isolate x)

Now, we replace the value of  for  and solve
 
 (Distribute)
 (Add  to both sides)
So  is equal to 

Let's try the second equation

 (Add  to both sides)

The value of  would be  and when solving both equations, we get the same value for  which is 

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