The first equation is correct. I think you want for the second equation.
Lisa is four times older than Anne.
In 5 years, Lisa will be 3 times older than Anne.
How old are Lisa and Anne?
I've tried setting it up two ways: and then solving for x which grants me x=-5.
I've also tried which also delivers the answer x=-5. Obviously Anne is not -5 years old.
Notice that the question asked "How old are Lisa and Anne". Just answering "x= 10" would NOT be acceptable. You started by saying that "Lisa is four times older than Anne" turned into y= 4x so apparently you are saying that Annes current age is 10 and Lisa's current age is 4(10)= 40.
By the way, I would argue that y= 4x would be "Lisa is four times as old as Anne". I would interpret "Lisa is four times older than Anne" as meaning that the difference between Anne and Lisa's age is four times Anne's age. That would translate to y- x= 4x or y= 5x.